Neural networks with sinusoidal activations have been proposed as an alternative to networks with traditional activation functions. Despite their promise, particularly for learning implicit models, their training behavior is not yet fully understood, leading to a number of empirical design choices that are not well justified. In this work, we first propose a simplified version of such sinusoidal neural networks, which allows both for easier practical implementation and simpler theoretical analysis. We then analyze the behavior of these networks from the neural tangent kernel perspective and demonstrate that their kernel approximates a low-pass filter with an adjustable bandwidth. Finally, we utilize these insights to inform the sinusoidal network initialization, optimizing their performance for each of a series of tasks, including learning implicit models and solving differential equations.

Solving large complex partial differential equations (PDEs), such as those that arise in computational fluid dynamics (CFD), is a computationally expensive process. This has motivated the use of deep learning approaches to approximate the PDE solutions, yet the simulation results predicted from these approaches typically do not generalize well to truly novel scenarios. In this work, we develop a hybrid (graph) neural network that combines a traditional graph convolutional network with an embedded differentiable fluid dynamics simulator inside the network itself. By combining an actual CFD simulator (run on a much coarser resolution representation of the problem) with the graph network, we show that we can both generalize well to new situations and benefit from the substantial speedup of neural network CFD predictions, while also substantially outperforming the coarse CFD simulation alone.

We present a differentiable physics engine that can be integrated as a module in deep neural networks for end-to-end learning. As a result, structured physics knowledge can be embedded into larger systems, allowing them, for example, to match observations by performing precise simulations, while achieves high sample efficiency. Specifically, in this paper we demonstrate how to perform backpropagation analytically through a physical simulator defined via a linear complementarity problem. Unlike traditional finite difference methods, such gradients can be computed analytically, which allows for greater flexibility of the engine. Through experiments in diverse domains, we highlight the system's ability to learn physical parameters from data, efficiently match and simulate observed visual behavior, and readily enable control via gradient-based planning methods.

We present a differentiable physics engine that can be integrated as a module in deep neural networks for end-to-end learning. As a result, structured physics knowledge can be embedded into larger systems, allowing them, for example, to match observations by performing precise simulations, while achieves high sample efficiency. Specifically, in this paper we demonstrate how to perform backpropagation analytically through a physical simulator defined via a linear complementarity problem. Unlike traditional finite difference methods, such gradients can be computed analytically, which allows for greater flexibility of the engine. Through experiments in diverse domains, we highlight the system's ability to learn physical parameters from data, efficiently match and simulate observed visual behavior, and readily enable control via gradient-based planning methods. Code for the engine and experiments is included with the paper.

We present a differentiable physics engine that can be integrated as a module in deep neural networks for end-to-end learning. As a result, structured physics knowledge can be embedded into larger systems, allowing them, for example, to match observations by performing precise simulations, while achieves high sample efficiency. Specifically, in this paper we demonstrate how to perform backpropagation analytically through a physical simulator defined via a linear complementarity problem. Unlike traditional finite difference methods, such gradients can be computed analytically, which allows for greater flexibility of the engine. Through experiments in diverse domains, we highlight the system's ability to learn physical parameters from data, efficiently match and simulate observed visual behavior, and readily enable control via gradient-based planning methods. Code for the engine and experiments is included with the paper.