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Autoregressive next-step prediction models have become the de-facto standard for building data-driven neural solvers to forecast time-dependent partial differential equations (PDEs). Denoise training that is closely related to diffusion…

Identifying parameters in partial differential equations (PDEs) represents a very broad class of applied inverse problems. In recent years, several unsupervised learning approaches using (deep) neural networks have been developed to solve…

Uncertainty estimation is a key component in any deployed machine learning system. One way to evaluate uncertainty estimation is using "out-of-distribution" (OoD) detection, that is, distinguishing between the training data distribution and…

Learning dynamical systems from incomplete or noisy data is inherently ill-posed, as a single observation may correspond to multiple plausible futures. While physics-based ensemble forecasting relies on perturbing initial states to capture…

Many modern large-scale machine learning problems benefit from decentralized and stochastic optimization. Recent works have shown that utilizing both decentralized computing and local stochastic gradient estimates can outperform…

When training deep neural networks, it is typically assumed that the training examples are uniformly difficult to learn. Or, to restate, it is assumed that the training error will be uniformly distributed across the training examples. Based…

We present a novel model Graph Neural Stochastic Differential Equations (Graph Neural SDEs). This technique enhances the Graph Neural Ordinary Differential Equations (Graph Neural ODEs) by embedding randomness into data representation using…

This paper presents a novel neural network training approach for faster convergence and better generalization abilities in deep reinforcement learning. Particularly, we focus on the enhancement of training and evaluation performance in…

Uncertainty estimation is crucial for machine learning models to detect out-of-distribution (OOD) inputs. However, the conventional discriminative deep learning classifiers produce uncalibrated closed-set predictions for OOD data. A more…

The rapid progress in machine learning in recent years has been based on a highly productive connection to gradient-based optimization. Further progress hinges in part on a shift in focus from pattern recognition to decision-making and…

Statistical (machine learning) tools for equation discovery require large amounts of data that are typically computer generated rather than experimentally observed. Multiscale modeling and stochastic simulations are two areas where learning…

The identification of a mathematical dynamics model is a crucial step in the designing process of a controller. However, it is often very difficult to identify the system's governing equations, especially in complex environments that…

Existing customization methods require access to multiple reference examples to align pre-trained diffusion probabilistic models (DPMs) with user-provided concepts. This paper aims to address the challenge of DPM customization when the only…

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…

In conventional ODE modelling coefficients of an equation driving the system state forward in time are estimated. However, for many complex systems it is practically impossible to determine the equations or interactions governing the…

Deterministic neural networks (NNs) are increasingly being deployed in safety critical domains, where calibrated, robust, and efficient measures of uncertainty are crucial. In this paper, we propose a novel method for training non-Bayesian…

Recent studies have shown that ensemble approaches could not only improve accuracy and but also estimate model uncertainty in deep learning. However, it requires a large number of parameters according to the increase of ensemble models for…

Even for the gradient descent (GD) method applied to neural network training, understanding its optimization dynamics, including convergence rate, iterate trajectories, function value oscillations, and especially its implicit acceleration,…

Uncertainty estimation is a crucial aspect of deploying dependable deep learning models in safety-critical systems. In this study, we introduce a novel and efficient method for deterministic uncertainty estimation called Discriminant…

We develop a probabilistic framework for deep learning based on the Deep Rendering Mixture Model (DRMM), a new generative probabilistic model that explicitly capture variations in data due to latent task nuisance variables. We demonstrate…