Accelerated Training of Physics Informed Neural Networks (PINNs) using Meshless Discretizations

We present a new technique for the accelerated training of physics-informed neural networks (PINNs): discretely-trained PINNs (DT-PINNs). The repeated computation of partial derivative terms in the PINN loss functions via automatic differentiation during training is known to be computationally expensive, especially for higher-order derivatives. DT-PINNs are trained by replacing these exact spatial derivatives with high-order accurate numerical discretizations computed using meshless radial basis function-finite differences (RBF-FD) and applied via sparse-matrix vector multiplication. The use of RBF-FD allows for DT-PINNs to be trained even on point cloud samples placed on irregular domain geometries. Additionally, though traditional PINNs (vanilla-PINNs) are typically stored and trained in 32-bit floating-point (fp32) on the GPU, we show that for DT-PINNs, using fp64 on the GPU leads to significantly faster training times than fp32 vanilla-PINNs with comparable accuracy. We demonstrate the efficiency and accuracy of DT-PINNs via a series of experiments. First, we explore the effect of network depth on both numerical and automatic differentiation of a neural network with random weights and show that RBF-FD approximations of third-order accuracy and above are more efficient while being sufficiently accurate. We then compare the DT-PINNs to vanilla-PINNs on both linear and nonlinear Poisson equations and show that DT-PINNs achieve similar losses with 2-4x faster training times on a consumer GPU. Finally, we also demonstrate that similar results can be obtained for the PINN solution to the heat equation (a space-time problem) by discretizing the spatial derivatives using RBF-FD and using automatic differentiation for the temporal derivative. Our results show that fp64 DT-PINNs offer a superior cost-accuracy profile to fp32 vanilla-PINNs.

Beyond modeling: NLP Pipeline for efficient environmental policy analysis

As we enter the UN Decade on Ecosystem Restoration, creating effective incentive structures for forest and landscape restoration has never been more critical. Policy analysis is necessary for policymakers to understand the actors and rules involved in restoration in order to shift economic and financial incentives to the right places. Classical policy analysis is resource-intensive and complex, lacks comprehensive central information sources, and is prone to overlapping jurisdictions. We propose a Knowledge Management Framework based on Natural Language Processing (NLP) techniques that would tackle these challenges and automate repetitive tasks, reducing the policy analysis process from weeks to minutes. Our framework was designed in collaboration with policy analysis experts and made to be platform-, language- and policy-agnostic. In this paper, we describe the design of the NLP pipeline, review the state-of-the-art methods for each of its components, and discuss the challenges that rise when building a framework oriented towards policy analysis.