Combining Microscopy Data and Metadata for Reconstruction of Cellular Traction Forces Using a Hybrid Vision Transformer-U-Net

Traction force microscopy (TFM) is a widely used technique for quantifying the forces that cells exert on their surrounding extracellular matrix. Although deep learning methods have recently been applied to TFM data analysis, several challenges remain-particularly achieving reliable inference across multiple spatial scales and integrating additional contextual information such as cell type to improve accuracy. In this study, we propose ViT+UNet, a robust deep learning architecture that integrates a U-Net with a Vision Transformer. Our results demonstrate that this hybrid model outperforms both standalone U-Net and Vision Transformer architectures in predicting traction force fields. Furthermore, ViT+UNet exhibits superior generalization across diverse spatial scales and varying noise levels, enabling its application to TFM datasets obtained from different experimental setups and imaging systems. By appropriately structuring the input data, our approach also allows the inclusion of metadata, in our case cell-type information, to enhance prediction specificity and accuracy.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates

Neural PDE surrogates can improve the cost-accuracy tradeoff of classical solvers, but often generalize poorly to new initial conditions and accumulate errors over time. Physical and symmetry constraints have shown promise in closing this performance gap, but existing techniques for imposing these inductive biases are incompatible with the staggered grids commonly used in computational fluid dynamics. Here we introduce novel input and output layers that respect physical laws and symmetries on the staggered grids, and for the first time systematically investigate how these constraints, individually and in combination, affect the accuracy of PDE surrogates. We focus on two challenging problems: shallow water equations with closed boundaries and decaying incompressible turbulence. Compared to strong baselines, symmetries and physical constraints consistently improve performance across tasks, architectures, autoregressive prediction steps, accuracy measures, and network sizes. Symmetries are more effective than physical constraints, but surrogates with both performed best, even compared to baselines with data augmentation or pushforward training, while themselves benefiting from the pushforward trick. Doubly-constrained surrogates also generalize better to initial conditions and durations beyond the range of the training data, and more accurately predict real-world ocean currents.