On the feasibility of foundational models for the simulation of physical phenomena

TL;DR

An exhaustive study of foundation models for the simulation of physical phenomena, with emphasis on continuum (solid and fluid) mechanics, to see to what extent they can undergo severe changes in domain shape, boundary conditions, and/or constitutive laws and still provide robust and accurate results.

Abstract

We explore the feasibility of foundation models for the simulation of physical phenomena, with emphasis on continuum (solid and fluid) mechanics. Although so-called learned simulators have shown some success when applied to specific tasks, it remains to be studied to what extent they are able to undergo severe changes in domain shape, boundary conditions and/or constitutive laws and still provide robust (i.e., hallucination-free) and accurate results. In this paper we perform an exhaustive study of these features, put ourselves in the worst-case scenario and study their resistance to such strong changes in their domain of application.

Figures (9)

• Figure 1: Pipeline illustration of the temporal integrator framework. Feature Engineering (green block), Encoder-Processor-Decoder (white blocks) and Integrator (orange block).
• Figure 2: Snapshots of the rollout for trajectory in $\mathcal{D}_{\text{test}}$, unseen geometry and boundary conditions. Loading was applied from $t=0$ to $t=330$, while unloading occurred from $t=330$ to $t=450$. Top: prediction. Bottom: ground truth.
• Figure 3: Snapshots of the rollout for trajectory in $\mathcal{D}_{\text{extra}}$, unseen boundary conditions and geometry out-of-distribution. Loading was applied from $t=0$ to $t=330$, while unloading occurred from $t=330$ to $t=450$. Top: prediction. Bottom: ground truth.
• Figure 4: The box plots display the distribution of the accumulated error per trajectory over 450-step rollouts. Each point on the plot represents the error an individual trajectory. a) Root mean squared error for position $\boldsymbol{q}$ and von Mises stress $\sigma_{\text{VM}}$. b) Relative root mean squared error for position $\boldsymbol{q}$ and von Mises stress $\sigma_{\text{VM}}$.
• Figure 5: Sketch of the transfer learning approach. A model trained to provide von Mises stresses as output variable is modified so as to provide the whole stress tensor field at a negligible cost.