Related papers: A scalable deep learning approach for solving high…
In this paper, we investigate the use of the deep learning method for solving a well-known NP-hard single machine scheduling problem with the objective of minimizing the total tardiness. We propose a deep neural network that acts as a…
We present two effective methods for solving high-dimensional partial differential equations (PDE) based on randomized neural networks. Motivated by the universal approximation property of this type of networks, both methods extend the…
Many large scale problems in computational fluid dynamics such as uncertainty quantification, Bayesian inversion, data assimilation and PDE constrained optimization are considered very challenging computationally as they require a large…
Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…
We propose numerical algorithms for solving large deformation diffeomorphic image registration problems. We formulate the nonrigid image registration problem as a problem of optimal control. This leads to an infinite-dimensional partial…
This work introduces a novel discontinuity-tracking framework for resolving discontinuous solutions of conservation laws with high-order numerical discretizations that support inter-element solution discontinuities, such as discontinuous…
Neural ordinary differential equations (NODE) have garnered significant attention for their design of continuous-depth neural networks and the ability to learn data/feature dynamics. However, for high-dimensional systems, estimating…
Routing problems are a class of combinatorial problems with many practical applications. Recently, end-to-end deep learning methods have been proposed to learn approximate solution heuristics for such problems. In contrast, classical…
Deep learning classifiers are now known to have flaws in the representations of their class. Adversarial attacks can find a human-imperceptible perturbation for a given image that will mislead a trained model. The most effective methods to…
We develop a distributed algorithm for convex Empirical Risk Minimization, the problem of minimizing large but finite sum of convex functions over networks. The proposed algorithm is derived from directly discretizing the second-order…
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…
Recent deep models for solving routing problems always assume a single distribution of nodes for training, which severely impairs their cross-distribution generalization ability. In this paper, we exploit group distributionally robust…
Seeking to improve model generalization, we consider a new approach based on distributionally robust learning (DRL) that applies stochastic gradient descent to the outer minimization problem. Our algorithm efficiently estimates the gradient…
The power and flexibility of Optimal Transport (OT) have pervaded a wide spectrum of problems, including recent Machine Learning challenges such as unsupervised domain adaptation. Its essence of quantitatively relating two probability…
In this paper we establish a connection between non-convex optimization methods for training deep neural networks and nonlinear partial differential equations (PDEs). Relaxation techniques arising in statistical physics which have already…
Inspired by the Boltzmann kinetics, we propose a collision-based dynamics with a Monte Carlo solution algorithm that approximates the solution of the multi-marginal optimal transport problem via randomized pairwise swapping of sample…
This paper establishes a continuous time approximation, a piece-wise continuous differential equation, for the discrete Heavy-Ball (HB) momentum method with explicit discretization error. Investigating continuous differential equations has…
Classical numerical methods for solving partial differential equations suffer from the curse dimensionality mainly due to their reliance on meticulously generated spatio-temporal grids. Inspired by modern deep learning based techniques for…
Entropic regularization provides a generalization of the original optimal transport problem. It introduces a penalty term defined by the Kullback-Leibler divergence, making the problem more tractable via the celebrated Sinkhorn algorithm.…
Efficient algorithms for solving optimal transport problems are important for measuring and optimizing distances between functions. In the $L^2$ semi-discrete context, this problem consists of finding a map from a continuous density…