On the Value of Tokeniser Pretraining in Physics Foundation Models

Physics foundation models are an increasingly popular approach for building versatile emulators for spatiotemporal systems. They require tokenisation layers that lift physical field data into a latent representation suitable for dynamic processing. A typical choice for this layer is a convolutional encoder, which lifts field information in a locality-aware way and can be trained very efficiently. However, this choice cannot be applied to a large class of scientific computing problems where data are represented on unstructured meshes, for example simulations on domains with curved boundaries. Such data typically require graph neural network architectures, which are more expensive to train and, in the form currently used, encode information differently from their CNN counterparts, thus limiting the portability of physics emulators between these data regimes. In this work we introduce Mesh-Native Convolution (MNC), a locality-aware tokenisation layer that encodes unstructured mesh-based data in a way that is analogous to CNNs. This approach leads to models that can be trained once on mesh data and then deployed to arbitrary unstructured meshes, even if these are irregular, with minimal retraining. We show that this tokenisation approach can be used to retrofit grid-pretrained foundation models efficiently on unstructured meshes and provide theoretical results to confirm the consistency of this approach with classical CNN encoders. We demonstrate the favourable performance of this retrofitting approach, which in many cases reaches acceptable accuracy even in zero-shot deployment, and outperforms existing baselines after only a few epochs of fine-tuning, thus providing an efficient bridge between the two data regimes.

Recent physics foundation models claim general spatiotemporal forecasting ability, yet their evaluations often collapse performance into a single average score under a fixed training distribution. This makes it difficult to determine whether a model has learned generalizable physical dynamics or only performs well under particular settings. We construct a benchmark with 8 physical dynamics, 3 training-data mixtures, and 25 test regimes induced by dynamic-scale and initial-condition complexity shifts, covering in-distribution, distribution-shift, and out-of-distribution settings. We evaluate five physics foundation model architectures and four model variants per architecture (scratch and three pretrained sizes), resulting in 60,000 measurements. Our results show that current physics foundation models behave as conditional rather than universal generalists: their generality depends on the physical regime, temporal scale, initial-condition setting, pretraining, model size, and architecture. Improving the training data distribution only partially mitigates this limitation. Pretraining and scaling are also unable to reliably remove their ability biases. We argue that improving physics foundation models requires moving beyond scaling models or expanding data, toward learning mechanisms that better capture transferable physical knowledge across regimes, temporal scales, and distribution shifts.

Scientific foundation models (SciFMs) aim to learn generalizable representations of physical systems governed by partial differential equations (PDEs), enabling transfer across tasks and domains. While physics-informed methods, which leverage PDE residuals as supervisory signals, have shown promise in scientific machine learning (SciML) for improving accuracy and reducing data requirements, their potential in the context of SciFMs remains relatively unexplored. In this evaluation study, we investigate whether (and how) physics-informed pre-training improves the generalization, robustness, and data efficiency of SciFMs. We conduct systematic experiments across a diverse set of PDEs, ranging from simple problems with periodic boundary conditions to more challenging systems such as the Navier-Stokes equations and non-periodic geometries. Our results show that physics-informed pre-training provides clear benefits in nice,'' e.g., structured, well-aligned settings: it enhances generalization and reduces data dependence, compared to data-only pre-training. However, these advantages diminish significantly as the downstream tasks become harder,'' e.g., as they involve discontinuities or deviate from the pre-training distribution. In complex or structurally different problems, such as those involving new boundary conditions or PDE operators, physics-informed models may perform only on par with---or even worse---than data-driven baselines. While residual-based pre-training helps in idealized regimes, realizing broadly transferable SciFMs will likely require subtler spatiotemporal inductive biases and more principled integration of physical knowledge into model architectures.