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In this paper we propose a novel deep neural network that is able to jointly reason about 3D detection, tracking and motion forecasting given data captured by a 3D sensor. By jointly reasoning about these tasks, our holistic approach is…

For many systems in science and engineering, the governing differential equation is either not known or known in an approximate sense. Analyses and design of such systems are governed by data collected from the field and/or laboratory…

We propose a Pretrained Finite Element Method (PFEM),a physics driven framework that bridges the efficiency of neural operator learning with the accuracy and robustness of classical finite element methods (FEM). PFEM consists of a physics…

This paper presents a partial differential equation framework for deep residual neural networks and for the associated learning problem. This is done by carrying out the continuum limits of neural networks with respect to width and depth.…

We develop a method to learn physical systems from data that employs feedforward neural networks and whose predictions comply with the first and second principles of thermodynamics. The method employs a minimum amount of data by enforcing…

A significant advancement in Neural Network (NN) research is the integration of domain-specific knowledge through custom loss functions. This approach addresses a crucial challenge: how can models utilize physics or mathematical principles…

Deep convolutional neural networks (CNNs) have been shown to perform extremely well at a variety of tasks including subtasks of autonomous driving such as image segmentation and object classification. However, networks designed for these…

We present the Finite Element Neural Network Interpolation (FENNI) framework, a sparse neural network architecture extending previous work on Embedded Finite Element Neural Networks (EFENN) introduced with the Hierarchical Deep-learning…

Humans have a remarkable capacity to understand the physical dynamics of objects in their environment, flexibly capturing complex structures and interactions at multiple levels of detail. Inspired by this ability, we propose a hierarchical…

We propose a new approach, called as functional deep neural network (FDNN), for classifying multi-dimensional functional data. Specifically, a deep neural network is trained based on the principle components of the training data which shall…

Despite significant effort in understanding complex systems (CS), we lack a theory for modeling, inference, analysis and efficient control of time-varying complex networks (TVCNs) in uncertain environments. From brain activity dynamics to…

Deep learning has become a pivotal technology in fields such as computer vision, scientific computing, and dynamical systems, significantly advancing these disciplines. However, neural Networks persistently face challenges related to…

When learning dynamical systems from data, embedding physical structure can constrain the solution space and improve generalization, but many physics-informed models assume access to the full system state. This limits their use in partially…

Differential equations are widely used to describe complex dynamical systems with evolving parameters in nature and engineering. Effectively learning a family of maps from the parameter function to the system dynamics is of great…

The dynamics of power grids are governed by a large number of nonlinear differential and algebraic equations (DAEs). To safely operate the system, operators need to check that the states described by these DAEs stay within prescribed limits…

This paper presents FDNet: a Focal Decomposed Network for efficient, robust and practical time series forecasting. We break away from conventional deep time series forecasting formulas which obtain prediction results from universal feature…

The task of video prediction is forecasting the next frames given some previous frames. Despite much recent progress, this task is still challenging mainly due to high nonlinearity in the spatial domain. To address this issue, we propose a…

Simulations of complex physical systems are typically realized by discretizing partial differential equations (PDEs) on unstructured meshes. While neural networks have recently been explored for surrogate and reduced order modeling of PDE…

$\partial\mathbb{B}$ nets are differentiable neural networks that learn discrete boolean-valued functions by gradient descent. $\partial\mathbb{B}$ nets have two semantically equivalent aspects: a differentiable soft-net, with real weights,…

Flow map learning (FML), in conjunction with deep neural networks (DNNs), has shown promises for data driven modeling of unknown dynamical systems. A remarkable feature of FML is that it is capable of producing accurate predictive models…