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Engineering monograph · Physics & machine learning

The Physics-AI Stack
surrogates

A plain-words, comprehensive guide to the physics-AI tools: what they are, how they learn, how to put them inside an agent that catches faults and predicts failures, what each one costs, the hardware you need, and a glossary for every term.

The whole story, briefly

Some AI does not chat. It learns to imitate a physics simulator so closely that it answers in milliseconds what used to take a supercomputer hours. NVIDIA has built a full ladder of these tools, from a fast engine at the bottom to ready-made models at the top.

This guide explains every rung in everyday language, shows how a software agent can lean on them to watch a machine and predict when it will fail, and lays out plainly what is free, what is paid, and the hardware you need. Read it top to bottom, or jump to any section. A glossary at the end defines every piece of jargon the moment you need it.

Section 01

Two ways AI can do physics

When people say "AI that understands physics," they usually mean one of two very different things. Keeping them apart is the whole game, because they fail and succeed in opposite ways.

The first kind is a reasoner. A large language model reads your problem in plain English, recognizes that it is, say, a spring-mass-damper or a second-order system, writes down the right equations, and explains the method step by step. It is excellent at framing a problem and choosing an approach, because it has read millions of worked examples. It is poor at being the calculator. Ask it for an exact settling time or a specific eigenvalue and it will hand you a confident, often wrong, number, because underneath it is predicting plausible text, not running arithmetic.N1

The second kind is a surrogate. This is not a language model at all, and it does not use words. It is a network trained to copy the input-to-output behavior of a real physics solver. You feed it the same kind of inputs the slow solver would take, a shape, a set of conditions, a load, and it returns a close answer almost instantly. It does not reason about the problem. It has simply seen so many already-solved cases that it can fill in a new one by interpolation, the way you can guess a person's weight from their height without a formula if you have seen enough people. Everything NVIDIA ships under the "physics-AI" banner is this second kind.

A quick side-by-side

Imagine asking both about a motor: "what temperature will this winding reach after ten minutes at full load?" The reasoner will correctly tell you it is a heat-balance problem, name the equation, and explain that the answer depends on losses and cooling, then guess a number you should not trust. The surrogate, if it was trained on thermal simulations of motors like this one, will return an actual temperature field in milliseconds that is usually close to what the slow solver would have produced. Neither is "smarter." They are different machines for different jobs.

Figure 1 · interactive
Reasoner or surrogate? Flip the switch.

Tap each option. The reasoner thinks in language and should call a tool to compute. The surrogate is that tool's fast stand-in. The best systems use both: the reasoner decides what to compute, the surrogate or the real solver computes it.

There is also a third, newer idea worth naming: a world model, an AI trained to predict how a whole scene changes over time, used mostly to generate practice data for robots. It sits closer to the surrogate family than the reasoner, and NVIDIA's version is called Cosmos. We will meet it briefly in the products section, but the two-way split above is the one to keep in your head.

Plain definition A surrogate model is a stand-in. You run the slow, accurate simulation many times to make training data, then train a network to predict the simulation's answer directly. After that you mostly call the cheap stand-in, and only run the real simulation now and then to check it is still right.
Section 02

The stack, rung by rung

The physics-AI offerings are not one product. They are four layers that build on each other, from raw physics math at the bottom to ready-to-use models at the top. Each layer hides the messiness of the one below it.

A kitchen analogy: the engine is the stove and knives that do the actual cooking, the simulation world is the kitchen with its lighting and layout, the framework is the set of recipes and techniques for inventing new dishes, and the model shelf is the freezer of ready-made meals you just heat up. You can cook from scratch or grab a finished dish; most people do some of both.

Figure 2 · interactive
The four layers (top is most ready-to-use)
Click any layer. Read bottom-up: a fast engine computes forces, a world wraps it in graphics and digital twins, a framework trains imitators of slow solvers, and a model shelf hands you pre-trained imitators.

The split that actually matters

The useful mental line runs through the middle of the stack. The bottom two rungs compute physics directly: they are engines and simulators that solve the equations, step by step, the honest slow way (just very fast, on a GPU). The top two rungs imitate physics: they are machine-learning models, and the toolkit that trains them, that learned to skip the step-by-step work and jump to the answer. Marketing blurs this line. The engineering does not, and confusing the two is how people end up trusting a guess where they needed a calculation.

Two words you will keep seeing

A digital twin is a living simulation of a specific real thing, a particular motor, factory, or river, kept in sync with sensor data so you can test changes on the copy before touching the real one. OpenUSD is the shared file format that lets all these tools describe the same 3D scene and pass it around without translation, the way PDF lets any program open the same document. Both show up across the top three rungs.

Section 03

How a surrogate is trained

Two ingredients go in, a fast predictor comes out. The clever part is forcing the network to respect physics, not just memorize examples, so it stays sensible in situations it has not seen exactly.

Step one is gathering examples. You run the slow, trustworthy solver (or collect real sensor readings) for many different inputs, and you save each input together with the answer it produced. This is the training data: thousands of solved cases. Step two is showing those cases to a network over and over until it can predict the answer for an input on its own. Step three, the one that makes this physics-AI rather than plain curve-fitting, is the physics penalty: during training the network is also scored on whether its predictions obey the governing equations, not just whether they match the saved answers. That extra pressure keeps it honest in the gaps between the examples it saw.

Figure 3 · interactive flowchart
From governing equations to millisecond answers
Physics lawsPDEs, ODEs Solver datasims + sensors Train networkoperator / PINN Physics penaltypunish law-breaking Fast predict~milliseconds answer

The physics penalty (dashed) is what separates this from ordinary curve-fitting. The network is scored both on matching examples and on obeying the equations, so it stays sensible between the data points it saw.

The three kinds of surrogate network

Not all surrogates are built the same way. Three designs do most of the work, and they suit different problems. Tap through them below.

Figure 4 · interactive
Pick a network family
A rough rule of thumb: PINNs for clean equations with little data, neural operators when you want one model to cover many conditions, graph networks when the thing lives on a mesh of connected parts.

Whichever family you use, the trained surrogate carries a quiet risk: it is only as good as the range of examples it saw. If you ask it about something far from its training cases, it will still answer, confidently, and it may be wrong. Good practice is to train an ensemble, several surrogates instead of one, and watch how much they disagree. Wide disagreement is the model's way of admitting it does not know, which gives you an honest uncertainty band instead of false precision. The next section is about exactly this edge.

Section 04

Fast versus trustworthy

A surrogate is a brilliant deal right up to the edge of what it was trained on. Past that edge, you go back to the real solver. This single trade-off decides how you use the whole stack.

Why does a surrogate fail outside its training range? Because it never learned physics in the way a textbook teaches it. It learned the shape of the answers across the examples it saw. Inside that range, filling in a new case is interpolation, which networks are very good at. Outside it, the network is extrapolating, guessing beyond the edge of its experience, and there is nothing holding it to reality. The physics penalty helps, but it does not fully rescue a model asked about conditions it has never encountered.

Figure 5 · interactive
Drag toward conditions the surrogate never saw
in training data far outside error solver: steady, slow surrogate: fast
12%

Time to a result is not on this chart because it would not fit: a solver run is measured in hours, a surrogate call in milliseconds. Partners report speed-ups from tens to a few hundred times on specific workloads, best read as vendor figures on favorable cases, not guarantees.N3

How to use this safely

The discipline is simple to state. First, before trusting a surrogate, check that the question sits inside its training range; if it does not, fall back to the real solver. Second, use the surrogate for the wide, cheap search, screening thousands of candidates, then confirm only the handful of survivors with the slow, exact solver. Third, prefer surrogates that respect conservation laws (energy in equals energy out, mass is not created or destroyed), because a model that can quietly break those will mislead you in ways that are hard to spot. The agent that drives all of this sits outside the simulation and calls it as a tool; it never lives inside the thing it is supposed to check.

The rule that follows from this Never let the surrogate be the final word on a safety-critical number. Treat it as a brilliant scout, not a judge. It tells you where to look fast; the real solver confirms what you found.
Section 05

The four named products

The names map cleanly onto the stack. Here they are in order, with what each one actually is, who uses it, and where it fits.

PhysicsNeMo — the workshop

This is the foundation tool for building and training your own surrogates. It is open-source and built on PyTorch, the most common framework for machine learning, so it slots into work people already do. It does not hand you finished answers; it hands you the parts: ready-made versions of the three network families, the physics-penalty machinery, and the plumbing to train across many GPUs at once. Its name has changed twice, from SimNet to Modulus to PhysicsNeMo, which is why you will see all three in older articles.N4 Think of it as the bench where surrogates are made. Outside groups already use it in production; one example is a chip-design company speeding up heat simulation of processors.

Apollo — the shelf of finished tools

Announced in November 2025, Apollo is a family of pre-trained physics models you can pick up and use straight away, or fine-tune on your own data so they fit your exact problem. It spans six areas: chips and semiconductors, structural mechanics (how things bend and break), weather and climate, fluid dynamics (air and liquid flow), electromagnetics (antennas, interference), and multiphysics, where several effects interact at once, such as plasma and fusion. Under the hood the models mix the best current designs: neural operators, transformers, and diffusion models. If PhysicsNeMo is the workshop, Apollo is the shelf of ready-made imitators, and several large engineering and chip companies have started building on them.

Earth-2 — one giant digital twin

Earth-2 is a planet-scale weather and climate twin. Its two stars are FourCastNet, a global forecaster built on a Fourier-style neural operator that predicts the whole atmosphere fast, and CorrDiff, a generative model that takes a coarse, blurry forecast and sharpens it into fine local detail, the way an editor turns a rough sketch into a clean drawing. In early 2026 the Earth-2 model family was opened up further and folded in outside models from groups like Europe's ECMWF, Microsoft, and Google. Insurance and energy-risk firms use it to simulate thousands of storm scenarios cheaply, which is too expensive with traditional forecasting alone.

Omniverse, PhysX, and Newton — the world and its engine

Omniverse is the photorealistic, real-time simulation world where digital twins live, and Isaac Sim is its robotics edition, a virtual lab where robots can be tried and trained safely before touching real hardware. Underneath, the physics is computed by PhysX, and increasingly by Newton, a newer open engine built by NVIDIA together with Google DeepMind and Disney Research and handed to the Linux Foundation in 2025. Newton matters to anyone building a simulation sandbox because it is differentiable: you can ask it not only "what happens?" but "how would the outcome change if I nudged this input?", which lets you optimize a design or tune a controller by following that gradient, instead of trying options blindly.

Figure 6 · interactive
Which tool for which job?
Most real projects use more than one rung: a finished model to start, the workshop to fine-tune it, and the world to test the result in context.

One more name you may hear: Cosmos, NVIDIA's world model, generates realistic practice footage so robots can learn from far more situations than you could film in real life. It feeds the simulation world rather than replacing the surrogates, so it sits alongside this layer rather than on the shelf above.

Section 06

A health-monitoring agent

Now put the stack to work. In Prognostics and Health Management (PHM), the job is to watch a machine, catch faults early, and predict how long it has left. A surrogate makes two slow loops fast enough for a software agent to run them continuously.

The core move is to treat a trained surrogate as a fast forward model, a tool the agent can call whenever it needs to know "what should be happening right now?" A surrogate that predicts a machine's temperatures or magnetic fields in milliseconds turns diagnosis and life-prediction from overnight jobs into something the agent can run thousands of times before it commits to a single decision. The agent itself is the language model: it decides what to check, calls the surrogate as a tool, reads the result, and explains it. It does not do the physics; it orchestrates it.

Diagnosis: spotting and naming a fault

Start with a healthy-baseline surrogate, a model trained on the machine when it was working correctly. Run it alongside the real machine, feeding it the same conditions. The residual, the gap between what the sensors measure and what the healthy model predicts, is the anomaly signal. When the machine is healthy the residual is small noise. When something changes, the residual grows and develops a telltale pattern.

Detecting that something is wrong is the easy half. Naming what is wrong is fault isolation, and this is where the cheap surrogate earns its keep. The agent forms a short list of suspects, a worn bearing, a shorted winding turn, a failing power switch, a blocked coolant path, and simulates each one on the surrogate to see which produces a residual pattern that matches reality. The closest match is the likely cause. Because each simulation is nearly free, the agent can test many faults at many severities instead of guessing once. When two suspects fit equally well, that genuine ambiguity becomes a human-in-the-loop checkpoint or a request for one more specific measurement, rather than a coin flip.

Prognosis: predicting time left

Prognosis is forecasting how much useful life remains, often called remaining useful life, or RUL. First the agent tunes the surrogate to match the machine's present, slightly degraded state, a step called data assimilation. Then it rolls that tuned model forward in time under the loads the machine is expected to see, watching the damage grow. Run this once and you get a single guess. Run it across a spread of plausible future workloads, which the speed of the surrogate makes affordable, and you get a distribution: not "it will fail in 40 days," but "it will most likely fail in 35 to 50 days, and here is the chance it goes sooner." That honest confidence band is far more useful for planning maintenance than a lone number.

Figure 7 · interactive loop
The diagnosis-and-prognosis cycle
1 · Measurelive signals 2 · Predictbaseline surrogate 3 · Residualmeasured − predicted 4 · Isolatetest fault hypotheses 5 · Forecastroll forward → life 6 · Decideact or ask a human

The same surrogate serves both halves: as a baseline in step two, as a what-if engine in step four, and as a roll-forward model in step five. Step six closes the loop back to step one.

The guardrail, again

Everything from Section 04 applies here. Before the agent trusts the surrogate, it checks that the machine's current operating point sits inside the surrogate's training range. Outside it, the agent falls back to the real solver or flags the case for a human. Pairing the surrogate with an ensemble gives the life estimate an honest uncertainty band rather than false precision. These checks are not optional polish; they are what separates a useful health monitor from a confident liar.

Figure 8 · block diagram
An agent that calls physics, instead of guessing it
tool sandbox LLM agentdecides & explains call result python-controlexact transient / steady state trained surrogatefast thermal / EM fields Newton / Warpdifferentiable sandbox FEA / CFD solverground-truth check verify
The agent stays outside the sandbox and picks the right tool. For a clean linear system it calls a control library and gets an exact answer. For a heavy field problem it calls a surrogate for speed, then verifies the promising cases against the real solver.

The toolkit mapping: build the field surrogates in PhysicsNeMo, warm-start from an Apollo structural or electromagnetics family, serve the surrogate behind an inference endpoint the agent calls, and use Newton or Warp as the differentiable substrate. Plain control questions, the transient and steady state of a given system, still go to a real control solver, because that is exact and cheap. The surrogates earn their place only where the honest alternative is an overnight run.

Takeaway The surrogate does not replace your physics. It makes the slow simulations around the machine fast enough that an agent can use them in a loop, while the agent stays a step removed, deciding and checking rather than computing.
Section 07

What is free, what it costs

The pattern across the whole stack is the same: the software and the model weights are mostly free, and you pay only when you use the optimized production-serving layer or redistribute the closed runtime.

A few terms make the pricing readable. Inference means running a trained model to get answers (as opposed to training it in the first place). NIM is NVIDIA's pre-packaged way of running a model for production, a container with the model and a fast engine already wired together behind a standard interface. The Open Model License is the permissive license most of NVIDIA's downloadable model weights ship under, which allows commercial use. And NVIDIA AI Enterprise is the paid support-and-license subscription you need to run NIM in production. With those in hand, the table below reads cleanly.

Figure 9 · interactive
Click a component to see its terms
open / free free to run, paid to serve or ship the one recurring cost
Everything you need to prototype an agent (the framework, the open model weights, the simulator, the engines, the free developer inference tier) costs nothing but the GPUs. The paid line item appears only at production scale.

So what would it actually cost?

The one recurring price is the production license, which is charged per GPU. There are two ways to pay it: a yearly license per GPU, or an hourly rate per GPU when you rent cloud GPUs. Which is cheaper depends entirely on how many hours a day you actually run. The estimator below does the arithmetic; slide it to your situation.

Figure 10 · interactive estimator
Rough yearly serving cost
4
8 h
Annual license
$0
Hourly at this use
$0

Illustrative only, using $2 per GPU per hour (NVIDIA AI Enterprise Essentials on-demand, mid-2026) and an illustrative $4,500 per GPU per year for the flat subscription. Licensing was restructured in 2026 and the annual figure is not publicly posted, so confirm with a partner; development on up to sixteen GPUs is free, so light or intermittent use may cost nothing.
The one recurring price Production inference through a packaged microservice needs an NVIDIA AI Enterprise license (now the "Essentials" tier). As of mid-2026 the on-demand cloud-marketplace rate is about $2 per GPU per hour; a flat per-GPU annual or multi-year subscription is also sold through partners by quote. It is priced per GPU, not per model or per token. Development and evaluation are free on up to sixteen GPUs. NVIDIA restructured this licensing in 2026 and prices change, so confirm a current quote before you budget.
Section 08

The hardware ladder

All of it runs on NVIDIA GPUs. That dependency, not the licensing, is the real lock-in. Two terms first, then what each tool needs, then a ladder from a laptop to a server.

CUDA is NVIDIA's software layer that lets programs run on its GPUs; "CUDA-capable" simply means an NVIDIA graphics card. VRAM is the memory on that card, and it is usually the limit that bites first: a model or a scene either fits in VRAM or it does not. Bigger jobs need more VRAM, which is the main reason data-center cards cost what they do. It also helps to know that training a model is far heavier than running a finished one, so you can serve a trained surrogate on modest hardware even if training it took a cluster.

What each tool needs

For building and training surrogates, PhysicsNeMo needs a CUDA-capable NVIDIA GPU on Linux and scales from a single GPU to multi-node clusters; serious training wants data-center cards. For serving pre-trained models such as Apollo or the Earth-2 models, the packaged inference layer supports data-center GPUs including H100, H200, A100, and L40S, with post-GTC-2026 profiles for the newer Rubin generation, and also runs on RTX workstations and PCs.

For the simulation world, Isaac Sim and Omniverse require an RTX GPU because of the ray-traced rendering, with 8 GB of VRAM as a floor and much more for complex scenes, on Windows or Linux. Newton and Warp need an NVIDIA GPU and run from Python.

Figure 11 · interactive
How far each rung gets you
A workstation card is enough to develop surrogates, run the simulator, and serve small endpoints. A data-center node is where real training and high-throughput serving live.

The practical takeaway: you can go a long way on a single good workstation. You only need the expensive hardware when you move from building and testing to training at scale and serving many requests at once. Renting that hardware by the hour in the cloud is a common middle path, so you are not forced to buy a server before you know you need one.

Section 09

Glossary of terms

Every piece of jargon in this guide, in one sentence each. Tap a term.

Figure 12 · interactive
Plain-words dictionary
Tap any term. These are working definitions meant for clarity, not formal precision.
Section 10

References & notes

Endnotes

N1A language model predicts the next word; it has no built-in arithmetic or convergence guarantee. It is reliable for choosing a method and unreliable for being the calculator. Pair it with a real solver and the weakness disappears.
N2A neural operator learns a map between whole functions rather than between single numbers, so one trained model generalizes across many conditions. The Fourier Neural Operator and DeepONet are the two best-known designs.
N3Reported speed-ups (tens of times for some modules, a few hundred times for fluid initialization) come from the vendors and their partners on chosen workloads. Treat them as plausible upper bounds, not typical results, and benchmark on your own case.
N4If you install it, the import path moved from modulus to physicsnemo, and the graph backend is migrating from DGL to PyTorch Geometric.

Sources

  1. NVIDIA, PhysicsNeMo developer page and project repository. developer.nvidia.com/physicsnemo · github.com/NVIDIA/physicsnemo
  2. NVIDIA, "NVIDIA Apollo Unveiled as Open Model Family" (SC25, Nov 2025). blogs.nvidia.com/blog/apollo-open-models
  3. NVIDIA Technical Blog, "Using AI Physics for TCAD Simulations" (Jan 2026). developer.nvidia.com/blog
  4. NVIDIA Newsroom and Meteorological Technology International on Earth-2 and the open Earth-2 model family (2024–2026). nvidianews.nvidia.com · meteorologicaltechnologyinternational.com
  5. NVIDIA, Omniverse and Isaac Sim documentation and repository. nvidia.com/en-us/omniverse · github.com/isaac-sim/IsaacSim
  6. Linux Foundation, "Contribution of Newton by Disney Research, Google DeepMind and NVIDIA" (Sep 2025). linuxfoundation.org/press
  7. NVIDIA, NIM for Developers and AI Enterprise licensing; per-GPU pricing and the developer free tier (2026 documentation and deployment guides). developer.nvidia.com/nim
  8. NVIDIA, Isaac Sim License FAQ (Apache 2.0 source; AI Enterprise required for redistribution). docs.isaacsim.omniverse.nvidia.com
  9. NVIDIA Open Model License (governs Apollo and other open weights; confirm on each model card). nvidia.com · huggingface.co
  10. Raissi, Perdikaris, Karniadakis, "Physics-Informed Neural Networks," J. Computational Physics (2019). Foundational PINN paper.
  11. Li et al., "Fourier Neural Operator" (2020); Lu et al., "DeepONet," Nature Machine Intelligence (2021); Kurth et al., "FourCastNet" (2023); Mardani et al., "CorrDiff" (2024).