What is Gimle?

Simulation Learning

After three decades of digital revolutions, the coming decades will be dominated by advances in physical world engineering. This will be driven by breakthroughs in computing that enable machines to reason about the physical world.

Computers are rapidly learning to reason. But reasoning is only half of the scientific method: for a complex physical system it gives you the hypothesis — an intuition for what might be true — not a way to test it. Simulation is the other half, the experiment: a way to test an intuition, explore where it leads, or even arrive at one in the first place. You simulate, see what holds, and evolve from there.

To reason about the physical world, a machine first has to model and simulate it, and as autonomous systems start to operate in it the gap becomes critical. You can't control what you can't simulate, or trust what you can't verify. Simulation, not reasoning, is the missing piece — and the next frontier of computing is the ability to run the experiment, not just form the hypothesis.

Giving machines that ability — combining formal methods, simulation and testing — is what we call simulation learning.

Learning Physics

Typically, we model physical systems in one of two ways.

Explicit modelling This is the traditional method of using hand-crafted governing equation that we believe are a good mathematical representation of real life physical systems.

This produces high fidelity, explicit models that are closely linked to the physical reality but it is very time-consuming, scales poorly with the complexity of systems and requires expert knowledge.

Implicit modelling The more modern approach of training a deep learnng system neural network to implicitly learn and approximate the dynamics of the system.

This approach is less time-consuming and scales better with complexity but the resulting black-box systems are brittle, require large amounts of data and provide minimal insight into the dynamics of the system.

Gimle takes a third path: we use learning to discover the explicit equations themselves. We don't train a model to be the system — we train it to understand and write the system. Or, put another way, we teach models to predict the structure of physical systems instead of the specific dynamics.

In the same way that understanding and predicting language teaches LLMs to understand the world projected through the language of humans, this ultimately teaches our models to understand physics through the language of dynamical systems.

Gimle

Gimle brings together formal methods, numerical simulation and large-scale machine learning under an agentic framework, allowing it to autonomously discover, simulate and verify models of the physical world.

At the base is a typed, category-theoretic, differentiable language for dynamical systems. Mathematical systems written in familiar notation are parsed into this representation, where they can be rewritten, compiled to high-performance simulation code, simulated and fitted to data. Every such system carries a constructive proof, and rewrites find closed-form solutions where they exist. One representation spans many calculi — deterministic, stochastic or discrete — and stays differentiable end-to-end, so models fit efficiently by gradient descent.

Built on this language is a foundation model for dynamics — a transformer that learns dynamical systems the way language models learn text, by learning to write them in our language for dynamical systems. From data, it discovers the explicit equations that govern a system, generalising across systems rather than being re-fit to each; and because the simulator generates its own training data, that data is effectively unlimited. The output is the equations themselves — interpretable and verifiable.

The model is trained in three stages:

• Next-token prediction — learn the language of dynamical systems on unlimited synthetic data; every output is a valid circuit by construction.
• Reinforcement learning — search the space of systems, guided by simulation-verified rewards. This trains on what circuits do, not just how they look.
• Iterative refinement — refine candidates toward exact target dynamics, like AlphaFold but for dynamical systems.

Because every model is an explicit, typed object rather than a black box, results are structured, composable and verifiable by construction — the model is the explanation.

Importantly, this scales the way LLMs do. A language model climbs a ladder — from the syntax of text, to its semantics, to a deep model of the world behind the language — and what carries it upward is scale. Models of physical dynamics will climb the same ladder: with scale they will move past the shallow symbolic fitting of methods toward an emergent, genuine understanding of physics. Adding to that, physics has an advantage text doesn't: the simulator is a built-in grader, so every candidate the model proposes can be run and checked against ground truth. That gives the kind of verifiable reward reinforcement learning needs to scale — something most domains simply don't have.

At the top of the stack, sits an agentic layer for long-running reasoning. These agents combine symbolic reasoning, simulation and the abilities of the transformer models beneath to solve dynamical-systems tasks end to end. Like discovering a system's governing equations from data, proving safety and stability properties or searching for control policies.

Each model and property that Gimle discovers and proves become a reusable, composable component — a self-expanding atlas of verified dynamics that compounds over time, built not by hand but by a machine that learns to see the structure behind the data.

Capabilities and Applications

Because a Gimle model is explicit rather than a black box, you can do a lot more with it than just query it:

• Discover & fit — recover governing equations from data, fit existing models, and compose large systems from verifiable sub-parts (explicit, approximate or learned).
• Simplify & solve — find simpler equivalent systems or closed-form solutions through rewriting and simulation.
• Simulate anything — any dynamical system, regardless of complexity, non-linearity, coupling or calculus.
• Prove properties — stability, reachability, safety and robustness, via formal and approximate methods.
• Control — test control strategies, explore extreme conditions, and find optimal policies.
• Keep models alive — continuously re-fit on new data and flag when reality diverges from the model.

These capabilities are most valuable in three situations: when a system is complex enough that finding its dynamics by hand is slow and painstaking; when the exact dynamics are intractable and what's needed is a simpler, faithful approximation; and when a model must be defended — to a regulator, board or auditor — where black-box ML can't be explained and legacy linear models miss the nonlinearities that matter. In each, Gimle offers explicit, verifiable structure you can interrogate and trust.

This has broad use across industries:

• Finance & economics — discover and fit stochastic models from market data, from instruments to the macro economy — explicit objects a risk team or supervisor can stress-test and defend.
• Life sciences & pharma — propose and fit mechanistic PK/PD and systems-biology models from sparse trial data, as regulators increasingly require.
• Risk & insurance — compose peril, geography and exposure into transparent, auditable catastrophe and actuarial models.
• Climate & carbon — fit auditable carbon-flux and earth-system models built to be checked rather than trusted.
• Energy & grids — fit differentiable battery, grid and generation models from operational data for forecasting and control.
• Engineering & fluids — discover fast, verifiable closed-form approximations of systems too expensive to solve directly, with provable guarantees.

Where this goes

LLMs began as autocomplete and became the layer everything built on language runs through. Similarly, Gimle begins as an alternative to symbolic regression and black-box neural simulators but becomes the intelligence layer for physics — not just prediction or approximation, but a true understanding of the physical world.