Bridging Physics and Machine Learning to Accelerate Engineering Breakthroughs

Multi-physics is a field of engineering that studies the simultaneous interaction of multiple physical phenomena. This approach contrasts with traditional, single-physics analysis by recognizing that in real-world systems, phenomena like fluid flow, heat transfer, structural mechanics, and electromagnetism are interconnected and influence each other. To illustrate how these complex interdependencies arise we examine an example from the field of fusion energy.

Achieving fusion energy remains one of the most ambitious challenges of our time, hindered by complex challenges in plasma physics, materials science, and energy systems. Today’s state-of-the-art simulators lack the predictive accuracy needed to confidently design fusion power plants.

The above can be very well summarized if we look at the problem of thermal conduction: in the heart of experimental fusion reactors, where hydrogen isotopes are heated to temperatures exceeding 150 million degrees Celsius, it is crucial to prevent this intense heat from escaping. Addressing this is a critical and complex challenge. The core of the problem lies in maintaining a sufficiently hot and dense plasma—a state of matter where electrons are stripped from their atoms—for a long enough duration to allow fusion to occur. However, the plasma's immense thermal energy naturally seeks to spread to cooler regions, through various mechanisms: turbulent transport within the plasma, preheat and loss of compression efficiency, direct transfer of heat to the outer wall. The mathematical description of these processes requires solving highly nonlinear differential equations, but the bottom line is that simple models of thermal conduction fail. 

Unfortunately, because of the complexity of solving the equations that describe the heat conduction, the common approach in many numerical simulations for fusion plasmas is to leave conduction as a free parameter that is adjusted to match available data. This is hardly satisfactory. Available data is sparse, and from sub-scale facilities. In many cases, the dependence of heat transport on plasma parameters is not measured; instead, what is known are measurable quantities that are only marginally affected by conductions. 

To address this challenge, fusion simulators need to embed the unknown physics (in this case, thermal conduction) by developing new capabilities. Adding physics-informed capabilities to a given simulator is what we refer to as “multi-physics”. The core idea behind multi-physics simulation is the coupling of different physical models. This means the output of one simulation becomes the input for another, and this exchange of information happens continuously throughout the simulation. In the fusion context that we have discussed, multi-physics means the coupling of a global (typically hydrodynamic) simulator to a high-fidelity solver of thermal conduction. In the same manner, one could envision adding many multi-physics packages to a fluid simulator such as

1. Electromagnetism, to be able to account for the effects of magnetic fields; 

2. Structural mechanics, to calculate induced stresses in materials; 

3. Radiation, to include energy carried by photons and their feedback on the matter. 

All of these components interact with each other, making accurate global simulations extremely challenging. In addition, each physics package employs expensive numerical solvers that are needed to maintain the accuracy, thus making such multi-physics simulations impractical even on the most advanced high-performance computing (HPC) facilities. This is why simplifications, as the ones used for thermal conduction are required, and even the most advanced simulations performed on El Capitan, a 11 millions cores HPC supercomputer (capable of performing at 1,700 PFlops/s) installed at the Lawrence Livermore National Laboratory (LLNL) are not able to fully predict what is happening on fusion experiment at the National Ignition Facility (NIF) laser at LLNL.

The way forward

A promising path forward is the integration of Artificial Intelligence (AI) and Machine Learning (ML) into physics-based simulation. By augmenting traditional, computationally efficient solvers—such as those used in fluid dynamics—with an advanced AI-driven multi-physics framework, we can dramatically enhance their capabilities. These AI-enhanced solvers, often built around neural networks (NN) trained on highly accurate simulation or experimental data, offer a powerful new approach to capturing the complex behaviours of fusion systems.

This is precisely the kind of research Mach42 is enabling. In our recent work, we have run a thermal conduction solver for thousands of different initial conditions. The idea here is to produce a dataset that is representative of different fusion plasma conditions. Once the dataset was generated, we successfully trained a Physics-Informed NN (PINN) to capture all the latent dependencies in the data. Details of this work are available here: https://arxiv.org/abs/2506.16619.

Of course, to be useful, the NN that we have developed also needs to be good enough to replace the actual heat conduction solver into the multi-physics approach discussed above. This essentially boils down to two properties. First, it needs to be able to capture all the relevant physical processes. Neural networks are not good at making extrapolations outside the data range used for training, hence the data must not only be accurate, but also be covering a sufficiently large parameter space. In the research that we have done, we have shown this is possible. The second requirement is that this multi-physics module must be able to correctly communicate with a fluid simulator. In particular, the NN needs to generalize over different implementations of the fluid simulations, including the ability of performing noise-free (or with noise that stays below the numerical noise of the fluid simulator) derivatives or other complex mathematical operations. This is very challenging and in many cases it is the bottleneck of these types of implementations. Mach42 scientists (in collaboration with colleagues at the University of Oxford), have recently shown (https://www.nature.com/articles/s41598-022-15416-y) that we can achieve these requirements if the NN surrogate is constructed using some specific physics constraints.

This work is at the early stages, but it shows a lot of promise already. If the integration between a thermal conduction NN with a fluid simulator is ultimately successful and able to provide better predictive capabilities, the path for the future is clear. The same technique can train accurate NN’s for electromagnetism, radiation, material stresses, etc. 

This surrogate modelling technique enables rapid exploration of a wide range of operational scenarios, without the heavy computational burden of high-fidelity simulations. A neural network learns the complex underlying physics and delivers precise results orders of magnitude faster. The goal of having a reliable simulator for fusion that does not require HPC access and can be deployed by fusion companies for yield optimization of their designs is now within reach.

This is not new for Mach42. The methodology is similar to how complex electronic components are modelled in circuit simulators, where a trained NN (e.g., a surrogate model in Verilog-A format) can replace detailed component models to dramatically speed up simulations. By embedding targeted, AI-powered precision within a fast simulation framework, we can bridge the gap in predictive capabilities — accelerating both the path to commercially viable fusion energy and the design and verification of next-generation electronic circuits.