--- title: "Engineering and technology · Simulations · Simulation Hypothesis" url: https://simulation-hypothesis.com/simulations/engineering description: "Airflow over wings, structures under load, chips before fabrication, robots before construction. Part of a taxonomy of the simulations people actually run." license: https://creativecommons.org/licenses/by/4.0/ credit: "Ross Allan Dahl, Simulation Hypothesis (simulation-hypothesis.com)" --- [Simulations](https://simulation-hypothesis.com/simulations)domain 9 of 18 # Engineering and technology Airflow over wings, structures under load, chips before fabrication, robots before they are built. Almost nothing gets built today without simulating it first. Over the past fifty years, simulation has replaced most physical prototypes. The oldest form, the physical scale model, is still in use. ## Flow ### Aerodynamics Air flowing over wings, cars, buildings and wind turbines. Question it answers: How much drag, how much lift, and where does the flow break away? Leaves out: Turbulence is modelled, not resolved, so fine separation detail is approximate. Runs on: about 10^15 FLOPS rough a university or corporate HPC cluster, days per case Since: 1962 Hess and Smith's panel method for aircraft shapes [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Turbulence Every eddy of a turbulent flow resolved directly, from the largest swirl down to the smallest. Question it answers: What is turbulence actually doing, so that cheaper models can approximate it? Leaves out: Limited to modest Reynolds numbers; real flows outrun the largest machines. Runs on: about 10^17 FLOPS rough a national supercomputer, a large share, for weeks Since: 1972 Orszag and Patterson's first 3D direct numerical simulation [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Physical scale models Wind tunnels, wave tanks, river models and shaking tables: the oldest simulations, and still used to check the numerical ones. Question it answers: Does the real flow match what the computer predicted? Leaves out: Scale effects mean a small model does not always behave like the full-size thing. Runs on: no computer. no digital computing; real air, water or a shaking table instead Since: 1871 Frank Wenham built one of the first wind tunnels [Physical analogue](https://simulation-hypothesis.com/simulations/methods#m-analogue)floor: Fields ### Cavitation simulation Bubbles forming and collapsing violently in fast-moving liquid, around ship propellers, pumps and valves. Question it answers: Where will cavitation erode this propeller or pump, and how do we design around it? Leaves out: Bubble collapse happens on scales finer than most simulations can afford to resolve everywhere. Runs on: about 10^15 FLOPS rough a university or shipyard cluster, hours per case Since: 1988 by 1988, early computational models of cavitating flow around propellers [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Multiphase and pipeline flow Oil, gas, water and slurries moving together through pipelines, wells and process plant. Question it answers: Will the pipeline run smoothly, or will slugs of liquid and gas choke it? Leaves out: Sudden slug formation is still one of the harder things to predict reliably. Runs on: about 10^14 FLOPS rough an energy company's cluster, hours per pipeline case Since: 1979 by 1979, early multiphase flow models for offshore oil and gas pipelines [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Ice accretion simulation Supercooled water droplets freezing onto aircraft wings and wind turbine blades in flight or in the wind. Question it answers: How much ice will build up, and will de-icing keep up with it? Leaves out: Real cloud droplet sizes and mixed-phase ice vary more than standard test conditions assume. Runs on: about 10^14 FLOPS rough an aerospace lab cluster, hours per icing case Since: 1988 by 1988, early computational icing codes support aircraft certification [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Physics-informed neural networks A neural network is trained so that its outputs satisfy a governing differential equation and observed data at once. Question it answers: Can a network learn the solution of a PDE with little or no mesh? Leaves out: Training is slow and unreliable for stiff or turbulent problems. Runs on: about 10^13 FLOPS rough Gradient-based training with automatic differentiation Since: 2017 Physics informed deep learning, part I (2017) [source](https://arxiv.org/abs/1711.10561) [Learned emulators](https://simulation-hypothesis.com/simulations/methods#m-learned)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Fields ### Neural operators A network learns the map from a function, such as a boundary condition, to the solution of a PDE, so new inputs are answered in one pass. Question it answers: Can a trained model solve a whole family of PDEs instantly? Leaves out: Needs many solver runs for training and extrapolates poorly. Runs on: about 10^15 FLOPS rough Expensive data generation, then fast inference Since: 2019 DeepONet: learning nonlinear operators (2019), followed by Fourier neural operators (2020) [source](https://arxiv.org/abs/1910.03193) [Learned emulators](https://simulation-hypothesis.com/simulations/methods#m-learned)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Fields ### Graph-network learned simulators A graph neural network trained on simulation data steps particles or mesh nodes forward to mimic fluids, cloth and solids. Question it answers: Can a neural net replace a physics solver for fluids and deformable objects? Leaves out: Errors build up over long rollouts and conservation is not guaranteed. Runs on: about 10^14 FLOPS rough Training on solver data, faster rollout Since: 2020 Learning to simulate complex physics with graph networks (2020) [source](https://arxiv.org/abs/2002.09405) [Learned emulators](https://simulation-hypothesis.com/simulations/methods#m-learned)[Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)floor: Fields ### Learned fluid solvers A convolutional network replaces the pressure-projection step of a grid fluid solver to speed up smoke and liquid simulation. Question it answers: Can a trained network make an incompressible flow solver much faster? Leaves out: Stability and accuracy are only tested on flows similar to training. Runs on: about 10^12 FLOPS rough Training on solver data, fast inference Since: 2016 Accelerating Eulerian fluid simulation with convolutional networks (2016) [source](https://arxiv.org/abs/1607.03597) [Learned emulators](https://simulation-hypothesis.com/simulations/methods#m-learned)[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Lattice-gas automata for fluid flow Particles hopping on a lattice with simple collision rules that reproduce the flow of a liquid or gas in the large, with no fluid-mechanics equations built in. Question it answers: Can a fluid's flow emerge from simple particle rules on a lattice? Leaves out: Noise from discrete particles and lack of Galilean invariance limit accuracy, which is why it was replaced. Runs on: about 10^11 FLOPS rough bit-wise rules on a lattice with millions of sites. Since: 1986 Frisch, Hasslacher and Pomeau's lattice-gas automata for the Navier-Stokes equation. [source](https://doi.org/10.1103/physrevlett.56.1505) [Cellular automata](https://simulation-hypothesis.com/simulations/methods#m-cellular-automata)[Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)floor: Rules ### Lattice Boltzmann flow simulation Fluid represented by distributions of particle velocities on a lattice, which stream and collide to give flow in complex geometry such as porous rock or blood vessels. Question it answers: How does a fluid flow through a very complicated geometry? Leaves out: The method is limited to low Mach numbers, and boundary treatment needs care. Runs on: about 10^15 FLOPS rough billions of lattice cells on graphics or cluster hardware. Since: 1988 McNamara and Zanetti's use of the Boltzmann equation to simulate lattice-gas automata. [source](https://doi.org/10.1103/physrevlett.61.2332) [Lattice field theory](https://simulation-hypothesis.com/simulations/methods#m-lattice)[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Rarefied-gas direct simulation Molecules of a thin gas moved and collided at random, where the gas is too sparse to be a continuous fluid, as at the edge of space or inside tiny channels. Question it answers: How does a thin gas flow around a vehicle at the edge of the atmosphere? Leaves out: Each simulated particle stands for trillions of real ones, so statistical noise is high at low speeds. Runs on: about 10^14 FLOPS rough billions of simulated particles. Since: 1963 Bird's direct simulation of the approach to translational equilibrium in a rigid sphere gas. [source](https://doi.org/10.1063/1.1710976) [Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)floor: Molecules ### Wind-farm large-eddy simulation Turbulent air through a wind farm with the forces from each rotor added, to see how wakes interact and cut the power of turbines downwind. Question it answers: How much power does a wind farm lose to its own wakes? Leaves out: Turbine blades are replaced by force disks, and terrain and atmospheric stability change the results. Runs on: about 10^16 FLOPS rough large-eddy runs of a multi-kilometre domain with tens of turbines. Since: 2010 Calaf, Meneveau and Meyers's large-eddy simulation of fully developed wind-turbine array boundary layers. [source](https://doi.org/10.1063/1.3291077) [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Fields ### Fluid-structure interaction A moving fluid and a deforming body solved together, so flapping, vibration and flutter can be predicted for wings, bridges and valves. Question it answers: How does a flexible structure move in the flow around it? Leaves out: Mesh motion and strong added-mass effects make coupling expensive and sometimes unstable. Runs on: about 10^15 FLOPS rough coupled fluid and solid solvers iterated each step. Since: 1974 Hirt, Amsden and Cook's arbitrary Lagrangian-Eulerian method for flows at all speeds. [source](https://doi.org/10.1016/0021-9991%2874%2990051-5) [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Fields ### Fire dynamics large-eddy simulation Hot gas and smoke from a fire in a room, tunnel or building solved as a buoyant turbulent flow with simple combustion, to see how heat and fumes spread. Question it answers: How quickly will smoke fill this corridor, and when will people no longer see their way out? Leaves out: Combustion chemistry and soot are simplified, and real fuels, windows and furniture are only approximately described. Runs on: about 10^13 FLOPS rough days on a cluster for a large building fire. Since: 2000 McGrattan and colleagues' Fire Dynamics Simulator user's manual from the US National Institute of Standards and Technology. [source](https://doi.org/10.6028/nist.ir.6469) [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Fields ## Structures and machines ### Structural analysis Bridges, buildings, aircraft and parts under load, heat and vibration. Question it answers: Where is the weak point, and how much margin is left? Leaves out: Assumes idealised materials and loads; real defects are handled by margins, not physics. Runs on: about 10^14 FLOPS rough an engineering workstation or small cluster, hours per case Since: 1956 Turner, Clough, Martin and Topp's aircraft structural method [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Crash simulation Vehicles deforming in a collision, with virtual occupants inside. Question it answers: How do we protect the people inside? Leaves out: Occupant injury is estimated from dummy models, not real human tissue variability. Runs on: about 10^15 FLOPS rough an automaker's HPC cluster, hours per crash case Since: 1979 by 1979, national-laboratory explicit finite-element codes model vehicle impacts [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Multibody dynamics Machines as rigid parts joined by hinges, springs and gears: suspensions, engines, robot arms. Question it answers: Will the mechanism move as designed, and where do the loads go? Leaves out: Parts are treated as rigid or lightly flexible, missing fine vibration modes. Runs on: about 10^13 FLOPS rough an engineering desktop, minutes to hours Since: 1971 Sheth and Uicker's computer method for mechanism analysis [Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Bodies ### Acoustics and vibration Sound waves in rooms, engines and cities, and vibration in structures. Question it answers: Will this hall achieve good acoustic quality, and will this bridge resonate audibly? Leaves out: Struggles with low frequencies, where wave effects dominate over rays. Runs on: about 10^14 FLOPS rough a workstation or small cluster, hours per case Since: 1968 Krokstad and colleagues modelled room acoustics by ray tracing [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Fatigue and crack growth A structure's slow damage from millions of small load cycles, tracked as cracks that grow and eventually fail. Question it answers: How many years or flight hours before this part needs replacing? Leaves out: Real flaws from manufacturing are more varied than the idealised starting cracks assumed. Runs on: about 10^14 FLOPS rough an engineering workstation or small cluster, hours per part Since: 1968 by 1968, early fracture-mechanics fatigue-life computer codes [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Tribology and contact mechanics Friction, wear and lubrication between moving surfaces in bearings, gears and joints. Question it answers: How long will this bearing last, and how much energy does friction waste? Leaves out: Surface roughness at the microscopic scale is approximated, not measured for each part. Runs on: about 10^13 FLOPS rough an engineering desktop, hours per contact case Since: 1970 by 1970, early elastohydrodynamic lubrication computer models [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Topology optimisation Material added and removed from a design space under loads until the lightest stiff shape appears, with holes and struts the engineer never drew. Question it answers: What is the lightest shape that still carries this load? Leaves out: Optimal shapes are often hard to manufacture and may be fragile to loads that were not considered. Runs on: about 10^13 FLOPS rough finite-element solves inside an optimisation loop with millions of variables. Since: 1988 Bendsoe and Kikuchi's generation of optimal topologies in structural design using a homogenisation method. [source](https://doi.org/10.1016/0045-7825%2888%2990086-2) [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Fields ### Peridynamic fracture modelling A solid represented as points interacting at a distance, so cracks start, branch and merge without any crack path defined beforehand. Question it answers: How does a crack choose its path through a brittle material? Leaves out: The interaction range and failure law must be calibrated to the material. Runs on: about 10^14 FLOPS rough meshless runs with millions of nodes. Since: 2000 Silling's reformulation of elasticity theory for discontinuities and long-range forces. [source](https://doi.org/10.1016/s0022-5096%2899%2900029-0) [Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Orbital-debris and satellite-collision modelling Satellites, fragments and rocket bodies tracked through decades of collisions and decay to find whether they feed on themselves and close useful orbits. Question it answers: How many collisions before debris makes an orbit unusable? Leaves out: Small untracked fragments, future launches and mitigation behaviour are uncertain. Runs on: about 10^11 FLOPS rough long Monte Carlo runs over many orbit populations. Since: 1978 Kessler and Cour-Palais's collision frequency of artificial satellites and the creation of a debris belt. [source](https://doi.org/10.1029/ja083ia06p02637) [Stochastic processes](https://simulation-hypothesis.com/simulations/methods#m-stochastic)[Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)[System dynamics](https://simulation-hypothesis.com/simulations/methods#m-system-dynamics)floor: Rules ### Co-simulation of linked models Separate simulations of a motor, a gearbox, a controller and a battery, each built in its own tool, are run together by trading data at agreed time steps. Question it answers: Does the whole machine work when every subsystem model, built by different teams, runs together? Leaves out: Exchanging data at fixed steps adds numerical error, and a stiff coupling can become unstable. Runs on: about 10^10 FLOPS rough hours on a workstation for a vehicle cycle. Since: 2011 Blochwitz and colleagues' Functional Mock-up Interface for tool-independent exchange of simulation models. [source](https://doi.org/10.3384/ecp11063105) [Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)[Discrete event](https://simulation-hypothesis.com/simulations/methods#m-discrete-event)[Real time](https://simulation-hypothesis.com/simulations/methods#m-real-time)floor: Rules ## Electronics and computers ### Circuit simulation Every voltage and current in an electronic circuit, transistor by transistor. Question it answers: Does the circuit work, and how much power does it draw? Leaves out: Component models are fitted approximations; real silicon varies chip to chip. Runs on: about 10^13 FLOPS rough an engineering desktop, minutes per chip block Since: 1973 Nagel and Pederson's SPICE, a general circuit simulation program at Berkeley [Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Populations ### Chip logic simulation A digital chip design run one clock cycle at a time before it is manufactured. Question it answers: Does the chip compute the correct result before the cost of manufacture is incurred? Leaves out: Timing is approximated; a working simulation can still fail once manufactured. Runs on: about 10^14 FLOPS rough a design workstation or small server cluster, hours per run Since: 1965 by 1965, early gate-level simulators check digital logic designs [Discrete event](https://simulation-hypothesis.com/simulations/methods#m-discrete-event)[Rules and states](https://simulation-hypothesis.com/simulations/methods#m-rules)floor: Rules ### Electromagnetics Radio waves, light and fields around antennas, circuits and optical devices. Question it answers: How well does this antenna radiate, and does this device leak interference? Leaves out: Fine geometric detail near the mesh limit gets smoothed away. Runs on: about 10^14 FLOPS rough a workstation or cluster, hours per design Since: 1966 Kane Yee's finite-difference time-domain method [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Computer network simulation Packets flowing through routers, links and protocols. Question it answers: Can the network sustain twice the traffic? Leaves out: Simplifies real hardware quirks and traffic patterns seen in production networks. Runs on: about 10^13 FLOPS rough a desktop or small server, minutes to hours Since: 1964 Leonard Kleinrock's queueing analysis of packet networks [Discrete event](https://simulation-hypothesis.com/simulations/methods#m-discrete-event)floor: Rules ### Emulation and virtual machines One machine imitating another exactly, instruction by instruction, so that its software runs unchanged. Question it answers: Can we run this old or future system on the hardware we have? Leaves out: Runs slower than the real hardware unless carefully optimised. Runs on: about 10^12 FLOPS rough a desktop computer, real time or faster Since: 1963 by 1963, early instruction-set simulators test computer designs before they exist [Rules and states](https://simulation-hypothesis.com/simulations/methods#m-rules)floor: Rules ### Semiconductor device simulation Electrons and dopant atoms inside a single transistor, before it is turned into a circuit-level model. Question it answers: How will this transistor's shape and doping change how it switches? Leaves out: Simplifies quantum effects that matter most at the very smallest transistor sizes. Runs on: about 10^14 FLOPS rough a semiconductor company's cluster, hours per device Since: 1964 Gummel's numerical model of a bipolar transistor [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[First principles](https://simulation-hypothesis.com/simulations/methods#m-first-principles)floor: Atoms ### Network digital twins A virtual copy of a communication network, kept in sync with the real one, used to test changes before they are applied. Question it answers: What would happen to the network if this change were made? Leaves out: Fidelity depends on telemetry, and scale is limited. Runs on: about 10^12 FLOPS rough Packet-level or learned models Since: 2021 Digital twin networks: a survey (2021) [source](https://doi.org/10.1109/JIOT.2021.3079510) [Discrete event](https://simulation-hypothesis.com/simulations/methods#m-discrete-event)[Learned emulators](https://simulation-hypothesis.com/simulations/methods#m-learned)floor: Rules ### Optical lithography simulation Light passing through a mask onto a photosensitive film to predict the circuit patterns printed on a chip, including blur and resist chemistry. Question it answers: Will the pattern on a mask print as intended on a chip? Leaves out: Resist chemistry and stochastic photon effects at tiny sizes are approximated. Runs on: about 10^13 FLOPS rough full-chip simulation for a layer. Since: 1975 Dill's optical lithography exposure model of resist. [source](https://doi.org/10.1109/t-ed.1975.18158) [Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Semiconductor process simulation The fabrication steps of a transistor, implanting, diffusing and oxidising, followed to predict doping profiles and shapes before the device model. Question it answers: What dopant profile and shape does a given fabrication recipe produce? Leaves out: Point-defect and interface models need calibration against each new process. Runs on: about 10^12 FLOPS rough two- or three-dimensional diffusion and reaction solves. Since: 1979 Antoniadis and Dutton's models for computer simulation of complete IC fabrication processes. [source](https://doi.org/10.1109/t-ed.1979.19452) [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Atoms ### Processor thermal modelling Heat flowing through the layers of a chip and its package, driven by the changing power of functional blocks, to find hot spots and set throttling. Question it answers: Where does a processor overheat as its workload changes? Leaves out: The model uses power estimates, and package and cooling details are lumped. Runs on: about 10^8 FLOPS rough a compact thermal network that runs in seconds. Since: 2003 Skadron and colleagues' temperature-aware microarchitecture with a compact thermal model. [source](https://doi.org/10.1145/859618.859620) [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Fields ### Photonic-crystal band-structure calculation Light in a periodic arrangement of dielectric, solved for the frequencies that can and cannot propagate, to design waveguides and filters. Question it answers: Which colours of light can a periodic structure block? Leaves out: Perfect periodicity is assumed, so disorder, losses and finite size are added separately. Runs on: about 10^10 FLOPS rough plane-wave eigenvalue solves for each wave vector. Since: 1990 Ho, Chan and Soukoulis's demonstration of a photonic gap in periodic dielectric structures. [source](https://doi.org/10.1103/physrevlett.65.3152) [Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Stacked chip thermal modelling Heat moving through layers of silicon piled vertically and cooled by liquid between them, solved quickly enough to set the design of the stack. Question it answers: Can a stack of chips with channels of coolant keep every layer below its limit? Leaves out: Real chips have hot spots much smaller than the model's cells, so peak temperatures can be underestimated. Runs on: about 10^8 FLOPS rough minutes on a workstation. Since: 2010 Sridhar and colleagues' 3D-ICE compact transient thermal model for 3D chips with inter-tier liquid cooling. [source](https://doi.org/10.1109/iccad.2010.5653749) [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Fields ## Robotics and autonomy ### Robot simulation Robots with simulated sensors and motors in a physics engine, trained or tested before touching the real world. Question it answers: Will a controller learned in simulation work on the real robot? Leaves out: Contact and friction in the real world are still hard to match exactly. Runs on: about 10^13 FLOPS rough a desktop with a GPU, real time or faster Since: 1983 by 1983, early offline-programming simulators plan industrial robot arms [Real time](https://simulation-hypothesis.com/simulations/methods#m-real-time)[Learned emulators](https://simulation-hypothesis.com/simulations/methods#m-learned)floor: Bodies ### Autonomous vehicle testing Self-driving software driving millions of virtual kilometres through rare and dangerous scenarios. Question it answers: How does the system handle the situation that happens once in a million kilometres? Leaves out: Rare real-world scenarios are still hard to capture, however many virtual kilometres are driven. Runs on: about 10^15 FLOPS rough a fleet of cloud GPU servers, run in parallel Since: 2004 simulation support for the early US self-driving vehicle grand challenges [Real time](https://simulation-hypothesis.com/simulations/methods#m-real-time)[Agent-based](https://simulation-hypothesis.com/simulations/methods#m-agent-based)floor: Bodies ### Swarm robotics Many simple robots coordinating by local rules, often borrowed from insects. Question it answers: Can a hundred cheap robots do what one expensive one cannot? Leaves out: Simple simulated robots do not capture real sensor noise and battery limits. Runs on: about 10^12 FLOPS rough a laptop, simulating tens to hundreds of robots Since: 1989 Gerardo Beni's early work on swarm intelligence and cellular robotics [Agent-based](https://simulation-hypothesis.com/simulations/methods#m-agent-based)floor: Bodies ### Digital twins A simulation kept continuously in step with a real machine, plant or building using its live sensor data. Question it answers: What is about to fail, and what happens if we change this setting? Leaves out: Accuracy is bounded by the sensor data supplied to it; gaps and drift accumulate. Runs on: about 10^13 FLOPS rough a cloud server continuously updating a plant model Since: 2002 Michael Grieves proposed pairing a product with a live virtual model [Discrete event](https://simulation-hypothesis.com/simulations/methods#m-discrete-event)[Learned emulators](https://simulation-hypothesis.com/simulations/methods#m-learned)[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Bodies ### Planetary rover mobility A rover's wheels and arm interacting with loose soil and rock on another world, before it ever drives there. Question it answers: Will the rover get stuck, and can its arm reach the sample? Leaves out: Extraterrestrial soil is known from only a handful of landing sites, so its behaviour is extrapolated. Runs on: about 10^13 FLOPS rough a space agency's cluster, hours per terrain case Since: 1997 wheel-soil simulations supporting the first successful Mars rover [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[Real time](https://simulation-hypothesis.com/simulations/methods#m-real-time)floor: Bodies ### Exoskeleton and prosthetic control A wearable machine and a human body moving together, with the control system tuned before a person wears it. Question it answers: Will the device assist the wearer's movement, or work against it? Leaves out: Simulated bodies rarely capture one person's particular injury or gait exactly. Runs on: about 10^13 FLOPS rough a research lab desktop, real time per trial Since: 1990 by 1990, early powered-exoskeleton control simulations at research labs [Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)[Real time](https://simulation-hypothesis.com/simulations/methods#m-real-time)floor: Bodies ### GPU-parallel robot learning environments Thousands of simulated robots run at once on one GPU so that a reinforcement-learning policy can train in minutes. Question it answers: How quickly can a robot policy be learned using massive parallel simulation? Leaves out: Contact physics are simplified, so transfer needs care. Runs on: about 10^15 FLOPS rough Thousands of parallel physics environments on GPU Since: 2021 Isaac Gym: high performance GPU-based physics simulation for robot learning (2021) [source](https://arxiv.org/abs/2108.10470) [Real time](https://simulation-hypothesis.com/simulations/methods#m-real-time)[Learned emulators](https://simulation-hypothesis.com/simulations/methods#m-learned)floor: Bodies ### Domain-randomised sim-to-real training A policy is trained in a simulator whose looks and physics vary at random so it works in the real world. Question it answers: Can a policy trained only in simulation work on a real robot? Leaves out: Randomisation ranges must cover the real gap, which is hard to know. Runs on: about 10^14 FLOPS rough Large randomised training runs Since: 2017 Domain randomization for transferring deep neural networks from simulation to the real world (2017) [source](https://arxiv.org/abs/1703.06907) [Learned emulators](https://simulation-hypothesis.com/simulations/methods#m-learned)[Stochastic processes](https://simulation-hypothesis.com/simulations/methods#m-stochastic)floor: Bodies ### Differentiable physics simulation A physics engine written so that gradients flow back through contacts and motion, letting designs or controllers be tuned by gradient descent. Question it answers: How should this controller or design change to improve its outcome? Leaves out: Gradients through hard contacts are noisy or misleading. Runs on: about 10^12 FLOPS rough Backward passes through many simulation steps Since: 2016 A differentiable physics engine for deep learning in robotics (2016) [source](https://arxiv.org/abs/1611.01652) [Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)[Learned emulators](https://simulation-hypothesis.com/simulations/methods#m-learned)floor: Bodies ### Adversarial driving-scenario generation An optimiser perturbs the paths of other road users in recorded scenes to find situations in which a self-driving system fails. Question it answers: Which realistic situations make an autonomy stack fail? Leaves out: A scenario that makes the system fail may almost never occur on real roads, so it says little about how often failures happen. Runs on: about 10^13 FLOPS rough Many closed-loop simulation runs Since: 2021 AdvSim: generating safety-critical scenarios for self-driving vehicles (2021) [source](https://arxiv.org/abs/2101.06549) [Stochastic processes](https://simulation-hypothesis.com/simulations/methods#m-stochastic)[Learned emulators](https://simulation-hypothesis.com/simulations/methods#m-learned)floor: Bodies ### Open driving simulators with sensor models A game-engine world with traffic, weather and simulated cameras and lidar for developing and testing autonomous driving. Question it answers: How would a driving system see and act in varied conditions? Leaves out: Sensor and traffic realism do not match the real world exactly. Runs on: about 10^12 FLOPS rough Real-time rendering on GPUs Since: 2017 CARLA: an open urban driving simulator (2017) [source](https://arxiv.org/abs/1711.03938) [Real time](https://simulation-hypothesis.com/simulations/methods#m-real-time)[Rules and states](https://simulation-hypothesis.com/simulations/methods#m-rules)floor: Bodies ### Learned legged locomotion A reinforcement-learning policy is trained to walk and run for a legged robot in a physics simulator, then is moved to the real machine. Question it answers: Can a robot learn to walk in simulation and keep its balance on real ground? Leaves out: Foot contact, motor delays and ground softness differ from the model, so a policy that works in simulation may fail on the machine. Runs on: about 10^16 FLOPS rough hours to days of GPU time per gait. Since: 2018 Tan and colleagues' sim-to-real learning of agile locomotion for quadruped robots. [source](https://arxiv.org/abs/1804.10332) [Learned emulators](https://simulation-hypothesis.com/simulations/methods#m-learned)[Real time](https://simulation-hypothesis.com/simulations/methods#m-real-time)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Bodies ### Learned humanoid locomotion A neural controller is trained in simulation for a two-legged human-shaped robot to walk over many kinds of ground, using a history of its own senses to adapt. Question it answers: Can a humanoid walk outdoors on stairs, grass and slopes using a policy learned without any real trials? Leaves out: Falls of a full-size humanoid are dangerous and costly, so testing is cautious and the policy's limits are not mapped. Runs on: about 10^17 FLOPS rough days on a GPU cluster. Since: 2023 Radosavovic and colleagues' real-world humanoid locomotion with reinforcement learning. [source](https://arxiv.org/abs/2303.03381) [Learned emulators](https://simulation-hypothesis.com/simulations/methods#m-learned)[Real time](https://simulation-hypothesis.com/simulations/methods#m-real-time)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Bodies ### Drone flight simulation Small aircraft with rotors, sensors and cameras flying through rendered scenes under simulated wind and physics, to develop autonomy and test it safely. Question it answers: Will this flight software keep the drone stable and avoid obstacles before it ever leaves the ground? Leaves out: Aerodynamics close to the ground, in gusts and between obstacles is simplified, so edge cases appear only on a real drone. Runs on: about 10^12 FLOPS rough real time on a gaming-class GPU, or thousands of runs in parallel. Since: 2017 Shah and colleagues' AirSim, visual and physical simulation for aerial and ground vehicles. [source](https://arxiv.org/abs/1705.05065) [Real time](https://simulation-hypothesis.com/simulations/methods#m-real-time)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Bodies ### Learned drone racing A control policy is trained in simulation to fly a quadrotor through a racing course at the limit of its speed, then flown on the real aircraft. Question it answers: Can a learned controller fly faster than a human champion pilot? Leaves out: The course is known and well lit, so the policy is not shown to work in unknown places or poor conditions. Runs on: about 10^16 FLOPS rough days of GPU training in simulation. Since: 2023 Kaufmann and colleagues' champion-level drone racing with deep reinforcement learning. [source](https://doi.org/10.1038/s41586-023-06419-4) [Learned emulators](https://simulation-hypothesis.com/simulations/methods#m-learned)[Real time](https://simulation-hypothesis.com/simulations/methods#m-real-time)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Bodies ### Soft robot simulation A robot made of rubbery material is modelled as a deformable solid by finite elements fast enough to control it in real time. Question it answers: How must the air pressure in the chambers be changed so the soft arm reaches a given point? Leaves out: Rubber properties change with temperature and age, and the model's speed requires a coarse mesh. Runs on: about 10^9 FLOPS rough real-time on a workstation. Since: 2013 Duriez's control of elastic soft robots based on a real-time finite element method. [source](https://doi.org/10.1109/icra.2013.6631138) [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[Real time](https://simulation-hypothesis.com/simulations/methods#m-real-time)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Bodies ### Tactile sensor simulation The touch images that a camera-based skin sensor would capture when pressed on objects are rendered in simulation, so robot hands can learn to feel. Question it answers: Can a robot learn to handle objects by touch without wearing out real sensors? Leaves out: The gel's soft deformation is rendered approximately, so sim-to-real gaps are larger for fine texture. Runs on: about 10^10 FLOPS rough real-time on a gaming-class GPU. Since: 2020 Wang and colleagues' TACTO, a fast open-source simulator for vision-based tactile sensors. [source](https://arxiv.org/abs/2012.08456) [Real time](https://simulation-hypothesis.com/simulations/methods#m-real-time)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)[Learned emulators](https://simulation-hypothesis.com/simulations/methods#m-learned)floor: Bodies ## Spaceflight and energy ### Spacecraft trajectories Paths through the gravity of the Sun, planets and moons, including gravity assists. Question it answers: What is the cheapest route to this moon, and when do we launch? Leaves out: Assumes known gravity and no perturbations; real navigation still requires course corrections. Runs on: about 10^12 FLOPS rough a laptop, seconds per candidate trajectory Since: 1959 early trajectory computations for the first Moon missions [Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Bodies ### Atmospheric entry A spacecraft hitting the atmosphere at many kilometres a second, with the shock wave and heat around it. Question it answers: Will the heat shield survive? Leaves out: Rare flow chemistry at extreme speed is still an active source of uncertainty. Runs on: about 10^15 FLOPS rough a national or university HPC cluster, hours per case Since: 1958 by 1958, early ballistic-missile reentry heating calculations [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Batteries and fuel cells Ions and electrons moving through electrodes and electrolyte as a cell charges and ages. Question it answers: How can charging be made faster without accelerating degradation of the battery? Leaves out: Ageing over thousands of cycles is still extrapolated, not fully simulated. Runs on: about 10^14 FLOPS rough a university cluster, hours per cell design Since: 1993 Doyle, Fuller and Newman's porous-electrode battery model [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[First principles](https://simulation-hypothesis.com/simulations/methods#m-first-principles)floor: Fields ### Rocket engine simulation Hot combustion gas expanding through a rocket engine's nozzle, and the heat it dumps into the walls that must survive it. Question it answers: How much thrust does this engine produce, and will the nozzle and walls survive the heat? Leaves out: Combustion instability, where the flame itself starts to oscillate, is still hard to predict. Runs on: about 10^16 FLOPS rough a space agency or company's supercomputer share, hours per case Since: 1968 by 1968, early computational models of rocket combustion chambers [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Spacecraft thermal and power simulation Heat and electrical power moving through a satellite as sunlight, shadow and onboard equipment change. Question it answers: Will every part of the spacecraft stay within its safe temperature and power budget? Leaves out: Assumes surfaces age and degrade as expected, which years in orbit do not always confirm. Runs on: about 10^12 FLOPS rough a satellite engineer's desktop, minutes per orbit case Since: 1965 by 1965, early thermal-balance models for orbiting satellites [Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Bodies ### Solar and wind farm yield simulation Sunlight or wind over a year matched against a farm's panels or turbines to predict how much energy it will produce. Question it answers: How much electricity will this farm actually generate, and is it worth building? Leaves out: A single unusual weather year can still depart sharply from the long-term average. Runs on: about 10^12 FLOPS rough a developer's desktop, minutes per site Since: 1981 by 1981, early computer wind-resource assessment for wind farm siting [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[Stochastic processes](https://simulation-hypothesis.com/simulations/methods#m-stochastic)floor: Fields ### Mega-constellation collision risk Tens of thousands of satellites in shared low orbits are tracked against existing debris to estimate close approaches, avoidance manoeuvres and the effect of failures. Question it answers: How many collisions would a mega-constellation add, and how fast does it need to remove failed satellites? Leaves out: Future launch rates, failure rates and operator behaviour are assumptions, and small untracked fragments are poorly known. Runs on: about 10^14 FLOPS rough days on a cluster for decades of orbital evolution. Since: 2017 Radtke and colleagues' study of how mega-constellations interact with the space debris environment. [source](https://doi.org/10.1016/j.actaastro.2016.11.021) [Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)[Stochastic processes](https://simulation-hypothesis.com/simulations/methods#m-stochastic)floor: Rules ### Conjunction collision probability Two objects' predicted orbits, with their uncertainties, are used to compute the chance that they will hit when they pass close. Question it answers: Is it worth firing thrusters to dodge this close approach? Leaves out: Orbit uncertainties are often underestimated, and a single probability depends heavily on the assumed shape of the error. Runs on: about 10^6 FLOPS rough seconds per conjunction, run over thousands of objects. Since: 1999 Alfriend and colleagues' analysis of errors in probability of collision. [source](https://doi.org/10.1023/a:1010056509803) [Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)floor: Rules ## Manufacturing and materials processing ### Metal casting and solidification Molten metal filling a mould and freezing, tracked for where it fills badly or shrinks into a defect. Question it answers: Will this casting fill properly, and where will the defects form? Leaves out: Real furnace and mould conditions vary more than a single simulated pour. Runs on: about 10^14 FLOPS rough an engineering firm's cluster, hours per case Since: 1985 by 1985, early computer simulations of this manufacturing process [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Welding simulation Metal melting, mixing and cooling in the narrow zone around a weld, with the stresses that warp the finished part. Question it answers: Will the weld hold, and how much will the part distort afterward? Leaves out: Assumes clean, steady welding conditions that manual welding does not always provide. Runs on: about 10^14 FLOPS rough an engineering firm's cluster, hours per case Since: 1975 by 1975, early computer simulations of this manufacturing process [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Additive manufacturing simulation A part built up layer by layer by a moving heat source, tracking the heating, melting and residual stress this leaves behind. Question it answers: Will the finished part warp or crack, and how should it be oriented on the build plate? Leaves out: Full-part simulations at true resolution are still too slow for most production schedules. Runs on: about 10^14 FLOPS rough an engineering firm's cluster, hours per case Since: 1995 by 1995, early computer simulations of this manufacturing process [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Metal forming and stamping Sheet metal or a hot billet pressed, stamped or forged into its final shape. Question it answers: Will the metal crack or wrinkle before it reaches the final shape? Leaves out: Assumes a uniform starting sheet; real material batches vary more than that. Runs on: about 10^14 FLOPS rough an engineering firm's cluster, hours per case Since: 1980 by 1980, early computer simulations of this manufacturing process [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Machining simulation A cutting tool removing metal as chips, with the forces, heat and wear this produces. Question it answers: How fast can we cut without breaking the tool or ruining the surface finish? Leaves out: Tool wear over many parts is still mostly estimated from past experience, not first principles. Runs on: about 10^13 FLOPS rough an engineering firm's cluster, hours per case Since: 1982 by 1982, early computer simulations of this manufacturing process [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Injection moulding simulation Molten plastic filling a mould's cavities and cooling into its final shape. Question it answers: Will the mould fill evenly, and where will it warp or show defects? Leaves out: Real plastic batches vary in exactly how they flow, more than standard material data assumes. Runs on: about 10^13 FLOPS rough an engineering firm's cluster, hours per case Since: 1976 by 1976, early computer simulations of this manufacturing process [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields [◂ Human behaviour and society](https://simulation-hypothesis.com/simulations/human-society)[Cities, infrastructure and operations ▸](https://simulation-hypothesis.com/simulations/cities-operations)