Physics-informed machine learning

**Six sensors, one law.** A steady temperature field (black) observed by six noisy sensors (circles). Linear interpolation (dashed) misses the shape between sensors (RMSE 0.09). Adding the heat equation as a penalty, with the boundary values unknown, recovers it (RMSE 0.03).

Why put physics in the model

Data from the real world is scarce and noisy, but the laws it obeys are often known. Physics-informed models use that: they penalise the residual of a governing equation (physics-informed neural networks), learn the solution operator of a whole family of equations (neural operators), or differentiate through a simulator.

Digital twins

A digital twin is a simulation kept in sync with a real system through measurements. Physics-informed ML makes twins fast enough to run alongside the real thing, and trustworthy where measurements are thin.

Where this is heading

Pasteur Labs builds what it calls simulation intelligence: AI, differentiable physics and scientific computing in one platform. The Aurelia Institute designs habitats for space, such as its self-assembling TESSERAE structures, where full-scale testing on Earth is hard and design leans on models. That is the kind of problem I want to work on.

What I'm doing

[e.g. the FNO surrogate tutorial you're working through, and what you found.]

References

M. Raissi, P. Perdikaris and G. E. Karniadakis. Physics-informed neural networks. Journal of Computational Physics 378, 686–707, 2019.
G. E. Karniadakis et al. Physics-informed machine learning. Nature Reviews Physics 3, 422–440, 2021.
Z. Li et al. Fourier neural operator for parametric partial differential equations. ICLR, 2021.
A. Lavin et al. Simulation intelligence: towards a new generation of scientific methods. arXiv:2112.03235, 2021.