Physics fields learn in context: PhysICL predicts on new meshes without weight updates
Synopsis
An engineering design study holds only tens to hundreds of simulations, each on its own mesh, and conventional surrogates are retrained for every study. PhysICL is pretrained once on a procedural prior, then treats a few labeled simulations as context and predicts fields, with quantiles, directly at each query's own unstructured-mesh nodes in one forward pass, with no weight update. On five PLAID datasets unseen in pretraining its field error falls as context grows and drops below the nearest context simulation; on AhmedML surfaces its peak GPU memory stays at 4.27 GiB.
Interpretation
A single pretrained checkpoint, with no weight update, treats several labeled simulations as context and predicts physical fields, with quantiles, directly at the nodes of each query's own unstructured mesh. Earlier mesh surrogates, from reduced-order models such as MMGP to graph networks and transformer neural operators, are fitted per dataset, so every new design study needs a new fit. On five PLAID datasets never seen in pretraining, field error decreases monotonically as the context grows and, from a stated context size, is below the nearest context simulation on all five datasets and all three context draws.
The model cuts each mesh into a fixed number of patches, lets query patches read context patches, then lets each query node read context anchors, so prediction works on arbitrary meshes. Tabular foundation models organize context by columns and rows, whereas a simulation's input is a mesh with fields whose size and connectivity vary within one task. Each mesh is split into 1,024 patches by recursive inertial bisection and the encoder reads a stratified subsample of nodes, so peak prediction memory barely grows with the mesh: 4.27 GiB on AhmedML surfaces with a median of 1.1 million nodes, about twenty times the largest pretraining mesh, against 4.07 GiB on the 6,000-node meshes of 2D_MSHE.
All pretraining data is generated online by a procedural prior and no field is stored, so training cost is nearly independent of mesh node count. Earlier PDE foundation models mostly pretrain on existing datasets on regular grids and then fine-tune for the target task. The reported pretraining ran 34.8 hours on four H200 GPUs, drew 8.0 million episodes at about 64 episodes per second, and kept GPU utilization at 85 to 100 percent while 80 CPU cores generated episodes.
Perspective
The demonstrated scope is stationary tasks: five PLAID engineering simulation datasets, 28 tasks of the prior on unseen geometries, and AhmedML 3D surface meshes with a median of 1.1 million nodes; each output field is decoded alone, and scalar outputs go to a tabular regressor on its row tokens.
All results come from a single pretraining run, and spread over pretraining seeds is not measured; the prior's physical models are panel solvers and analytic laws rather than finite-element solutions, and in 3D only wings and blades have a physical model; per-dataset reduced-order models are more accurate where outputs lie near a low-dimensional linear space; on 2D_MSHE fine-tuning lowers error, but no control run continues pretraining for as many steps, so the gain is not separated from the extra steps.