Related papers: Learning Differential Equations that are Easy to S…

A universal rule-based self-learning approach using deep reinforcement learning (DRL) is proposed for the first time to solve nonlinear ordinary differential equations and partial differential equations. The solver consists of a deep neural…

Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…

A novel approach for supervised classification is presented which sits at the intersection of machine learning and dynamical systems theory. At variance with other methodologies that employ ordinary differential equations for classification…

Generative Adversarial Networks have recently shown promise for video generation, building off of the success of image generation while also addressing a new challenge: time. Although time was analyzed in some early work, the literature has…

Decision support systems often rely on solving complex optimization problems that may require to estimate uncertain parameters beforehand. Recent studies have shown how using traditionally trained estimators for this task can lead to…

We propose a novel framework for structured prediction via adversarial learning. Existing adversarial learning methods involve two separate networks, i.e., the structured prediction models and the discriminative models, in the training. The…

Much as replacing hand-designed features with learned functions has revolutionized how we solve perceptual tasks, we believe learned algorithms will transform how we train models. In this work we focus on general-purpose learned optimizers…

We propose a trainable-by-parts surrogate model for solving forward and inverse parameterized nonlinear partial differential equations. Like several other surrogate and operator learning models, the proposed approach employs an encoder to…

Deep learning involves a difficult non-convex optimization problem with a large number of weights between any two adjacent layers of a deep structure. To handle large data sets or complicated networks, distributed training is needed, but…

Recurrent neural networks have gained widespread use in modeling sequential data. Learning long-term dependencies using these models remains difficult though, due to exploding or vanishing gradients. In this paper, we draw connections…

Nonlinear optimization-based control policies, such as those those arising in nonlinear Model Predictive Control, have seen remarkable success in recent years. These policies require solving computationally demanding nonlinear optimization…

Small neural networks with a constrained number of trainable parameters, can be suitable resource-efficient candidates for many simple tasks, where now excessively large models are used. However, such models face several problems during the…

Temporal difference (TD) learning algorithms with neural network function parameterization have well-established empirical success in many practical large-scale reinforcement learning tasks. However, theoretical understanding of these…

Inspired by path-integral solutions to the quantum relaxation problem, we develop a numerical method to solve classical stochastic differential equations with multiplicative noise that avoids averaging over trajectories. To test the method,…

Adversarial training, in which a network is trained on both adversarial and clean examples, is one of the most trusted defense methods against adversarial attacks. However, there are three major practical difficulties in implementing and…

Many successful methods to learn dynamical systems from data have recently been introduced. However, ensuring that the inferred dynamics preserve known constraints, such as conservation laws or restrictions on the allowed system states,…

We study the use of Temporal-Difference learning for estimating the structural parameters in dynamic discrete choice models. Our algorithms are based on the conditional choice probability approach but use functional approximations to…

Neural Laplace is a unified framework for learning diverse classes of differential equations (DE). For different classes of DE, this framework outperforms other approaches relying on neural networks that aim to learn classes of ordinary…

We propose a novel training method based on nonlinear multilevel minimization techniques, commonly used for solving discretized large scale partial differential equations. Our multilevel training method constructs a multilevel hierarchy by…

Neural networks have shown promising potential in accelerating the numerical simulation of systems governed by partial differential equations (PDEs). Different from many existing neural network surrogates operating on high-dimensional…