After three decades of digital revolutions, the coming decades will be dominated by advances in physical world engineering - many of which will be enabled by breakthroughs in computing.
We believe that the next frontier of computing will be breakthroughs in how we simulate and reason about physical systems.
Why?
Today computers can reason about the world at the level of a junior domain expert - and perhaps soon at the level of a senior expert or scientist.
However, there is a big difference between reasoning/intuition and simulation/calculation - even the smartest scientists need large scale computing to calculate the outputs of their models, test their hypothesis and inform their intuition.
It is a fundamental difference.
Like in the case of human experts, a computer reasons based on its intuition, i.e. it uses its prior knowledge to extrapolate to its current context and situation, but, like human experts, to test its reasoning it needs to perform calculations.
When we are dealing with the physical world, this involves complex, large scale computations and simulations.
Therefore as we continue to push autonomous computing into the physical world, having systems that enables machines to automomously construct and simulate models of the physical world will become increasingly important.
Only then will computers be able to go beyond guessing and intuition.
And this goes beyond enabling computers to reason about concrete physical systems. More generally it also equips machines with the methods and tools needed to achieve scientific breakthroughs - enabling them to inform their reasoning through a mix of formal methods, simulations and testing, what we refer to as simulation learning.
Simulation Learning
We believe that the combination of formal methods, numerical simulations and agentic reasoning has the potential to revolutionise our ability to model, understand and control the physical world.
Traditionally we have modelled physical systems by painstakingly hand-crafting sets of governing equations that we believe are a good mathematical representation of real life physical systems.
This approach 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.
More recently, this highly manual process has been gradually replaced with deep learning approaches that implicitly learn the governing dynamics of the system.
These approaches are less time consuming and scale 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 real life system.
What is needed is a common interface for computers to construct, simulate, verify and combine explicit and implicit models of complex physical systems. Combined with modern reasoning capabilities this would enable computers to fully build and reason about real world systems.
Such abilities could have huge benefits for disciplines that work on complex systems design and analysis, like engineering, finance, biology, chemistry, climate science and more.
Gimle
Gimle is our project to build machines that can construct, simulate and reason about complex dynamical systems. At its core is a system that combines formal methods and proof theory, for rewriting and proving properties about systems, with numerical methods, for simulations and approximations of properties, and layers on top an agentic framework specialised in long-running, creative reasoning tasks.
It consists of four core elements:
Asgard: Dynamical Systems Foundation
Asgard makes the laws of dynamics executable. A system written in familiar mathematical notation compiles into a typed, differentiable circuit — a calculus-agnostic, category-theoretic representation in which composition, products and feedback are first-class, and that can be rewritten, reasoned about, simulated and fitted to data.
The flow runs end to end: a LEAN-style language describes and rewrites systems and bridges to existing domain knowledge, a compiler lowers them to circuits where — in the spirit of proofs-as-programs — rewrites prove, simplify or approximate, and a differentiable runtime simulates and optimises the result.
Highlights of Asgard:
- A constructive proof attached to every system, with equivalence-preserving rewrites that find and prove closed-form solutions where they exist.
- One circuit, many calculi: the same system runs under deterministic, stochastic or discrete semantics, differentiable end-to-end for gradient-based fitting.
- Hierarchical composition, with learned black-box models as leaf nodes where explicit definitions fall short.
- Property proofs and tolerance-bounded approximations via computational algebra, such as cylindrical algebraic decomposition.
Mimir: Foundational Model for Dynamical Systems
A transformer that learns the structure of dynamical systems the way language models learn the structure of text. From observed data, Mimir discovers the explicit equations that govern the system — a foundational model that generalises across many different systems rather than being re-fit to each.
What makes this work is the differentiable simulator of Asgard: the model only has to learn structure, while gradient descent through the simulator fills in the numeric constants. And because that simulator generates its own training data, the data is effectively unlimited — improving the generator directly improves the model.
Highlights of Mimir:
- It outputs the equations themselves — explicit, interpretable systems that can be analysed and verified — rather than a black-box approximation.
- Library-free and feedback-native: composition, products and feedback are first-class, so controllers and recurrences are represented as objects, not rediscovered as patterns.
- A single model spans many systems and calculi — deterministic, stochastic or discrete — instead of re-solving each from scratch.
- Inference-time search over the typed grammar refines proposals and recovers compact closed-form approximations of complex dynamics.
- Already effective at small scale: a single-GPU model recovers structure on synthetic and classical systems and out-extrapolates sparse-regression baselines by up to ~60× beyond the observed range — with the path forward being scale, not new principles.
Hugin: Agentic Framework for long-running reasoning tasks
Alongside these other components sits our agentic framework, Hugin, specialised in long running, creative reasoning tasks. Hugin is built to run large scale multi-agent reasoning that can use branching, long-term memory and complex tool calls to not just reason but also learn and improve over time.
Highlights of Hugin compared to other frameworks:
- The configuration of each LLM interaction is completely dynamic: dynamic tool and task configurations, dynamically templated prompts, dynamic context rendering and dynamic LLM selection.
- Native multi-agent support that can mix synchronous and asynchronous agent orchestration within the same sessions.
- The ability for agents to branch their reasoning flow, allowing them to perform rollouts and side-tasks.
- Support for memory both in context, through dynamic rendering, and longer term shared memory through artifacts.
Bifrost: Agents for reasoning about dynamical systems
Tying it all together is Bifrost. Bifrost is a set of agents, defined in Hugin, that can use the agentic framework and external LLMs to reason about and learn how to combine the capabilities of Asgard and Mimir.
With the use of symbolic reasoning, numerical simulations, computational algebraic methods and the foundational dynamical systems model of Mimir, Bifrost agents are able to combine formal syntactical reasoning, systems generation and numerical simulations to solve complex dynamical systems tasks.
Capabilities
With these components we can solve a number of important challenges in modelling and reasoning about complex real-life systems. Because every model is an explicit, typed object rather than a black box, the results are structured, composable and verifiable by construction — the model is the explanation.
Finding and fitting models to observed data
We can autonomously discover governing equations from observed data, fit existing models to new data, compose large complex systems from simpler, verifiable sub-systems either defined explicitly, as approximations or as learned black box systems.
Simplify and solve known systems
Automatically discover simpler equivalent systems or closed form solutions through circuit rewriting and numerical simulations.
Discover initial conditions and parameters that collapse existing models into simpler, more tractable systems.
Simulate any known systems
Simulate any dynamical system regardless of complexity, non-linearity, coupling, dimensionality or underlying calculus.
Reasoning about and proving properties of complex systems
Properties of systems, like stability, reachability, safety or robustness, can be reasoned about and proven using both formal methods and through approximate methods.
Controlling complex systems
Scenario simulations and formal verifications allow us to test control strategies, explore extreme or uncertain conditions and find optimal control policies.
Decomposing complex systems dynamics
The ability to combine systems that are both explicitly defined using the systems language and learned black-box models, allows us to decompose complex system dynamics into simpler, more interpretable components.
Keeping models alive on real-world data
Continuously fit and re-fit models as new data arrives, monitor live systems against their fitted dynamics, and surface when reality starts to diverge from the model.
Applications
Simulation learning is general, but it is most valuable in domains with a particular shape: where a model has to be defended — to a regulator, a board, an auditor or a reviewer; where the system is naturally built from coupled sub-systems; where data is sparse but mechanistic priors are strong; and where the underlying dynamics are real rather than metaphorical.
In these domains there are usually two options today, and both fall short: black-box machine learning is flexible but cannot be explained or defended, while the decades-old linear-statistical models that own the regulated landscape are defensible but cannot capture the nonlinearities that actually matter. Gimle offers a third option — explicit, verifiable structure that captures the real dynamics with the same audit trail as the linear models it replaces.
Finance and economics
Stochastic differential equations are already the gold standard in quantitative finance, and regulators increasingly demand models that can be explained.
Gimle discovers and fits them directly from market data — from individual instruments up through portfolios, factor models and the macro economy — producing an explicit object a risk team or supervisor can inspect, stress-test and defend.
Life sciences and pharmacology
Drug modelling — pharmacokinetics, pharmacodynamics and quantitative systems pharmacology — is built on compartmental and physiological ODE systems fitted from sparse trial data, with tools largely unchanged since the 1990s, even as regulators increasingly require mechanistic models in submissions.
Gimle can propose candidate structures from data, fit them, and produce the explicit, defensible models the approval process now expects — and the same applies across systems biology and reaction-network chemistry.
Risk and insurance
Catastrophe and actuarial models estimate losses from perils across geographies and assets, and insurers must justify them under regimes like Solvency II — often without being able to see inside the models they license.
A grammar that composes peril, geography and exposure the way an actuary already thinks, with each sub-model transparently fitted from data, turns an opaque legacy into something auditable.
Climate and carbon
Confidence in carbon markets and environmental reporting increasingly hinges on models that can be independently audited.
Gimle can fit mechanistic carbon-flux and earth-system models — forest, soil, wetland — that share one grammar and one diagnostic surface and are designed to be checked rather than trusted, alongside compositional reduction and scenario exploration of large coupled climate systems.
Energy and grids
Battery degradation, grid dynamics and renewable generation are governed by well-understood physics — equivalent-circuit and electrochemical models — but fitting them to real operational data is slow and hand-tuned.
Gimle fits these models, differentiable and composable from cell to pack to thermal behaviour, and simulates them forward for forecasting, optimisation and control.
Engineering and fluid dynamics
In fields like aerospace and mechanical engineering the governing equations are known but intractable — solving Navier-Stokes directly is far too expensive, so industry falls back on reduced models (LES, RANS) and hand-built closure approximations.
Gimle can discover fast, high-fidelity closed-form approximations of these systems: accurate enough to use inside a design loop, and explicit enough to hand to a certifying body as the equation.
The same machinery composes subsystems and proves properties such as stability, reachability and safety, so the surrogate carries guarantees a black-box model cannot.
These are just some of the domains where simulation learning can have real-world impact — wherever the systems are real, the structure matters, and the model has to be trusted.