Publications

Data-Driven Whitney Forms for Structure-Preserving Control Volume Analysis

We introduce a scientific machine learning framework adopting a partition of unity architecture to identify physically-relevant control volumes, with generalized fluxes between subdomains encoded via Whitney forms. The approach provides a differentiable parameterization of geometry which may be trained in an end-to-end fashion to extract reduced models from full field data while exactly preserving physics.

Jonas A Actor, Xiaozhe Hu, Andy Huang, Scott A Roberts, Nathaniel Trask

Journal of Computational Physics 496 (2024), 112520.

Unsupervised physics-informed disentanglement of multimodal data

We introduce physics-informed multimodal autoencoders (PIMA) - a variational inference framework for discovering shared information in multimodal datasets. Individual modalities are embedded into a shared latent space and fused through a product-of-experts formulation, enabling a Gaussian mixture prior to identify shared features.

Elise Walker, Nathaniel Trask, Carianne Martinez, Kookjin Lee, Jonas A Actor, Sourav Saha, Troy Shilt, Daniel Vizoso, Remi Dingreville, Brad L Boyce

Foundations of Data Science 7.1 (2025), 418-445.