Solving Voxelized Deformable Soft Bodies with Physics-Informed Neural Networks

This thesis explores the integration of Physics-Informed Neural Networks (PINNs) and Interaction Networks (INs) to simulate voxelized deformable soft-body systems, aiming to bridge the gap between computational efficiency and physical fidelity. The work begins with a theoretical overview of both PINNs and INs, followed by the development of a hybrid neural architecture that augments data-driven message passing with additional physics-based loss terms derived from governing differential equations.

The methodology incorporates soft physical constraints into the loss function, including force balance, spring dynamics, boundary constraints, and energy conservation. The deformable system is modeled as a two-dimensional spring-mass lattice subjected to external forces. Experiments are conducted on two benchmark systems: a damped harmonic oscillator and a 2D deformable lattice, with ground-truth trajectories generated using classical numerical solvers. The network is trained using supervised learning and further guided by physics-informed losses. All experiments are implemented in PyTorch, and optimized using the Adam optimizer.

The study uses fully synthetic data generated through well-understood mechanical models; no human or animal subjects are involved, and no IRB or ethical approval is required. While the proposed approach does not yet deliver stable simulation performance in large-scale voxelized systems, the results reveal failure modes and training bottlenecks that provide insights for future work on combining neural networks with physical priors for dynamic system modeling.