🔬“We have foundation models for language, not for physics” — Anima Anandkumar, Bren Professor of Computing

What It Covers

Caltech's Anima Anandkumar explains how neural operators — a generalization of neural networks that process continuous function spaces at any resolution — are replacing traditional physics simulations across weather forecasting, fusion plasma modeling, and carbon sequestration, running tens of thousands to one million times faster than classical supercomputer-based methods.

Key Questions Answered

• •Neural Operators vs. PINNs: Physics-Informed Neural Networks fail on time-dependent, turbulent systems like fluid dynamics because the optimization landscape becomes intractable. Neural operators solve this by training on existing data across many equation instances, then solving new instances at inference time — combining data-driven speed with optional physics constraints added as loss terms, enabling accurate predictions where PINNs collapse entirely.
• •Weather Forecasting Benchmark: ForecastNet, trained on roughly 50,000 global ERA5 reanalysis snapshots at 0.25-degree resolution, matches traditional numerical weather prediction accuracy while running tens of thousands of times faster — consumer-grade GPU versus supercomputer. The model predicts in six-hour autoregressive steps and correctly identified Hurricane Lee's landfall several days earlier than conventional forecasting systems.
• •Spherical Geometry for Climate Stability: Standard AI weather models assume a rectangular Earth projection, which causes runaway instability during long rollouts. Incorporating spherical harmonic bases into the Fourier neural operator architecture stabilizes multi-month to multi-year climate simulations. ForecastNet 3 is currently the only AI architecture functioning as a validated climate emulator, used by the Allen Institute for AI.
• •Ensemble Probabilistic Prediction: Deterministic single-trajectory forecasts are insufficient for extreme weather risk assessment. Running tens of independent ensemble members — each initialized with slightly perturbed conditions — produces calibrated probability distributions over hurricane tracks and heat events. AI weather models make large ensembles computationally feasible where traditional models cannot, enabling meaningful landfall probability estimates for emergency planning.
• •Fusion Plasma Digital Twins: Neural operators trained on magnetohydrodynamic simulation data from the UK Atomic Energy Agency model tokamak plasma evolution one million times faster than classical solvers. This speed enables real-time disruption prediction and opens pathways toward active magnetic field control to prevent plasma collapse — a critical barrier to sustained fusion energy that physical experiments alone cannot address cost-effectively.
• •TorchLean Verification Framework: Neural networks deployed in safety-critical control loops — drones, nuclear reactors — require formal robustness guarantees. TorchLean embeds PyTorch-style network definitions inside the Lean theorem prover, enabling certified robustness algorithms like CROWN to bound output sensitivity to input perturbations. The framework also quantifies finite-precision arithmetic errors, providing verifiable safety certificates before deployment in physical systems.