Related papers: Stability of implicit neural networks for long-ter…
Learning a stable Linear Dynamical System (LDS) from data involves creating models that both minimize reconstruction error and enforce stability of the learned representation. We propose a novel algorithm for learning stable LDSs. Using a…
We introduce implicit Bayesian neural networks, a simple and scalable approach for uncertainty representation in deep learning. Standard Bayesian approach to deep learning requires the impractical inference of the posterior distribution…
Neural ordinary differential equations (NODE) have been proposed as a continuous depth generalization to popular deep learning models such as Residual networks (ResNets). They provide parameter efficiency and automate the model selection…
Adversarial neural networks solve many important problems in data science, but are notoriously difficult to train. These difficulties come from the fact that optimal weights for adversarial nets correspond to saddle points, and not…
Physics-informed neural networks (PINNs) have shown promising potential for solving partial differential equations (PDEs) using deep learning. However, PINNs face training difficulties for evolutionary PDEs, particularly for dynamical…
Incorporating a priori physics knowledge into machine learning leads to more robust and interpretable algorithms. In this work, we combine deep learning techniques and classic numerical methods for differential equations to address two…
In this paper, we consider the problem of learning prediction models for spatiotemporal physical processes driven by unknown partial differential equations (PDEs). We propose a deep learning framework that learns the underlying dynamics and…
Long-term traffic flow forecasting plays a crucial role in intelligent transportation as it allows traffic managers to adjust their decisions in advance. However, the problem is challenging due to spatio-temporal correlations and complex…
Deep neural networks (DNNs), especially physics-informed neural networks (PINNs), have recently become a new popular method for solving forward and inverse problems governed by partial differential equations (PDEs). However, these methods…
Deep neural networks (NNs) are powerful black box predictors that have recently achieved impressive performance on a wide spectrum of tasks. Quantifying predictive uncertainty in NNs is a challenging and yet unsolved problem. Bayesian NNs,…
Pose Machines provide a sequential prediction framework for learning rich implicit spatial models. In this work we show a systematic design for how convolutional networks can be incorporated into the pose machine framework for learning…
Solving time-dependent partial differential equations (PDEs) is fundamental to modeling critical phenomena across science and engineering. Physics-Informed Neural Networks (PINNs) solve PDEs using deep learning. However, PINNs perform…
Deep convolutional neural networks have revolutionized many machine learning and computer vision tasks, however, some remaining key challenges limit their wider use. These challenges include improving the network's robustness to…
We propose to use deep learning to estimate parameters in statistical models when standard likelihood estimation methods are computationally infeasible. We show how to estimate parameters from max-stable processes, where inference is…
Neural Ordinary Differential Equations (N-ODEs) are a powerful building block for learning systems, which extend residual networks to a continuous-time dynamical system. We propose a Bayesian version of N-ODEs that enables well-calibrated…
Scaling deep reinforcement learning networks is challenging and often results in degraded performance, yet the root causes of this failure mode remain poorly understood. Several recent works have proposed mechanisms to address this, but…
Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…
Machine-learning technologies for learning dynamical systems from data play an important role in engineering design. This research focuses on learning continuous linear models from data. Stability, a key feature of dynamic systems, is…
Graph Neural Networks (GNNs) are widely used deep learning models that learn meaningful representations from graph-structured data. Due to the finite nature of the underlying recurrent structure, current GNN methods may struggle to capture…
Stability is a key property of both forward models and inverse problems, and depends on the norms considered in the relevant function spaces. For instance, stability estimates for hyperbolic partial differential equations are often based on…