Differentiable Simulations with Material Point Method
Keywords: DiffMPM
TL;DR: A differentiable MPM simulator enables gradient-based optimization for inverse problems in engineering design by integrating simulation, automatic differentiation, and machine learning.
Abstract: Solving optimization and inverse problems are critical for engineering design and analysis. Despite the computational power, calculating derivatives, i.e., evaluating the forward simulation multiple times with small perturbations, is computationally very expensive and is prone to numerical instability. Traditional forward simulations cannot be used in machine learning models for optimization, as they cannot compute gradients with respect to the input parameters (reverse mode). We propose a novel Differentiable Programming simulator that combines automatic reverse differentiation with a second-order gradient-based optimization algorithm, such as L-BFGS, to develop a fully-differentiable MPM simulator. Using the differentiable simulator, we can identify the input material properties by iteratively updating the input parameters by minimizing a loss function. Typically the loss function is the norm of the difference to the target observation. We then minimize this gradient (loss corresponding to the input parameters) using a second-order optimization algorithm. We compare our differentiable simulator results with the state-of-the-art Proximal Policy Optimization (PPO) algorithm in Reinforcement Learning. Differentiable MPM solves the exact PDE and can approximate the dynamics of its environment better than model-agnostic reinforcement learning methods. The differentiable MPM simulator is written in Google JAX and exploits Tensor Processing Units to accelerate the computational time. We successfully estimated the input parameters for a collision of two deformable bodies. The differentiable MPM is a novel tool to provide gradients through a simulator, which can be coupled with existing machine learning algorithms to generate real-time decisions and optimization in robotics.
Submission Number: 2
Loading