Solving Voxelized Deformable Soft Bodies with Physics-Informed Neural Networks

<p dir="ltr">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.</p><h4>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.</h4><h4>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.</h4><p></p>