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We propose a general framework for solving forward and inverse problems constrained by partial differential equations, where we interpolate neural networks onto finite element spaces to represent the (partial) unknowns. The framework…

We present our deep learning framework to solve and accelerate the Time-Dependent partial differential equation's solution of one and two spatial dimensions. We demonstrate DiffusionNet solver by solving the 2D transient heat conduction…

We propose a new data-driven method to learn the dynamics of an unknown hyperbolic system of conservation laws using deep neural networks. Inspired by classical methods in numerical conservation laws, we develop a new conservative form…

Modeling the traffic dynamics is essential for understanding and predicting the traffic spatiotemporal evolution. However, deriving the partial differential equation (PDE) models that capture these dynamics is challenging due to their…

Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and…

We develop a framework for estimating unknown partial differential equations from noisy data, using a deep learning approach. Given noisy samples of a solution to an unknown PDE, our method interpolates the samples using a neural network,…

There have been extensive studies on solving differential equations using physics-informed neural networks. While this method has proven advantageous in many cases, a major criticism lies in its lack of analytical error bounds. Therefore,…

The solution to partial differential equations using deep learning approaches has shown promising results for several classes of initial and boundary-value problems. However, their ability to surpass, particularly in terms of accuracy,…

Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…

We introduce a compositional physics-aware FInite volume Neural Network (FINN) for learning spatiotemporal advection-diffusion processes. FINN implements a new way of combining the learning abilities of artificial neural networks with…

We compare the Finite Element Method (FEM) simulation of a standard Partial Differential Equation thermal problem of a plate with a hole with a Neural Network (NN) simulation. The largest deviation from the true solution obtained from FEM…

In this paper, we propose a novel video depth estimation approach, FutureDepth, which enables the model to implicitly leverage multi-frame and motion cues to improve depth estimation by making it learn to predict the future at training.…

We consider the problem of forecasting complex, nonlinear space-time processes when observations provide only partial information of on the system's state. We propose a natural data-driven framework, where the system's dynamics are modelled…

In the pursuit of accurate experimental and computational data while minimizing effort, there is a constant need for high-fidelity results. However, achieving such results often requires significant computational resources. To address this…

We introduce Neural Dynamical Systems (NDS), a method of learning dynamical models in various gray-box settings which incorporates prior knowledge in the form of systems of ordinary differential equations. NDS uses neural networks to…

Predicting the evolution of systems that exhibit spatio-temporal dynamics in response to external stimuli is a key enabling technology fostering scientific innovation. Traditional equations-based approaches leverage first principles to…

System identification through learning approaches is emerging as a promising strategy for understanding and simulating dynamical systems, which nevertheless faces considerable difficulty when confronted with power systems modeled by…

In this paper, we propose the Deep Structured self-Driving Network (DSDNet), which performs object detection, motion prediction, and motion planning with a single neural network. Towards this goal, we develop a deep structured energy based…

Deep neural networks are powerful tools for solving nonlinear problems in science and engineering, but training highly accurate models becomes challenging as problem complexity increases. Non-convex optimization and sensitivity to…

The potential of neural networks (NN) in engineering is rooted in their capacity to understand intricate patterns and complex systems, leveraging their universal nonlinear approximation capabilities and high expressivity. Meanwhile,…