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In this paper we propose a new model-based unsupervised learning method, called VarNet, for the solution of partial differential equations (PDEs) using deep neural networks (NNs). Particularly, we propose a novel loss function that relies…

Machine Learning · Computer Science 2019-12-17 Reza Khodayi-Mehr , Michael M. Zavlanos

Designing proper loss functions for vision tasks has been a long-standing research direction to advance the capability of existing models. For object detection, the well-established classification and regression loss functions have been…

Computer Vision and Pattern Recognition · Computer Science 2021-02-10 Peidong Liu , Gengwei Zhang , Bochao Wang , Hang Xu , Xiaodan Liang , Yong Jiang , Zhenguo Li

Stochastic gradient descent (SGD) is a popular algorithm for optimization problems arising in high-dimensional inference tasks. Here one produces an estimator of an unknown parameter from independent samples of data by iteratively…

Machine Learning · Statistics 2023-06-23 Gerard Ben Arous , Reza Gheissari , Aukosh Jagannath

Learning the underlying potential energy of stochastic gradient systems from partial and noisy observations is a fundamental problem arising in physics, chemistry, and data-driven modeling. Classical approaches often rely on direct…

Machine Learning · Computer Science 2026-04-23 Yubin Lu , Xiaofan Li , Chun Liu , Qi Tang , Yiwei Wang

Calibration of large-scale differential equation models to observational or experimental data is a widespread challenge throughout applied sciences and engineering. A crucial bottleneck in state-of-the art calibration methods is the…

Optimization and Control · Mathematics 2021-02-23 Jon Cockayne , Andrew B. Duncan

Robust physics (e.g., governing equations and laws) discovery is of great interest for many engineering fields and explainable machine learning. A critical challenge compared with general training is that the term and format of governing…

Numerical Analysis · Mathematics 2021-02-15 Zhiming Zhang , Yongming Liu

This paper addresses Bayesian inference related to partial differential equations (PDEs), particularly nonparametric regression constrained by PDEs. To effectively encode prior information, we propose a novel framework that learns a…

Statistics Theory · Mathematics 2026-02-09 Junxiong Jia , Deyu Meng , Zongben Xu , Fang Yao

We introduce a new class of spatially stochastic physics and data informed deep latent models for parametric partial differential equations (PDEs) which operate through scalable variational neural processes. We achieve this by assigning…

Machine Learning · Computer Science 2023-06-08 Arnaud Vadeboncoeur , Ieva Kazlauskaite , Yanni Papandreou , Fehmi Cirak , Mark Girolami , Ömer Deniz Akyildiz

This article is concerned with the existence and the long time behavior of weak solutions to certain coupled systems of fourth-order degenerate parabolic equations of gradient flow type. The underlying metric is a Wasserstein-like…

Analysis of PDEs · Mathematics 2016-09-23 Daniel Matthes , Jonathan Zinsl

To enhance the reproducibility and reliability of deep learning models, we address a critical gap in current training methodologies: the lack of mechanisms that ensure consistent and robust performance across runs. Our empirical analysis…

Machine Learning · Computer Science 2026-01-05 Waqas Ahmed , Sheeba Samuel , Kevin Coakley , Birgitta Koenig-Ries , Odd Erik Gundersen

The Federated Learning setting has a central server coordinating the training of a model on a network of devices. One of the challenges is variable training performance when the dataset has a class imbalance. In this paper, we address this…

Machine Learning · Computer Science 2020-11-13 Dipankar Sarkar , Ankur Narang , Sumit Rai

Incorrectly labelled training data are frustratingly ubiquitous in both benchmark and specially curated datasets. Such mislabelling clearly adversely affects the performance and generalizability of models trained through supervised learning…

Machine Learning · Computer Science 2025-11-27 Nicholas Pellegrino , David Szczecina , Paul Fieguth

Stochastic Gradient Descent (SGD) based methods have been widely used for training large-scale machine learning models that also generalize well in practice. Several explanations have been offered for this generalization performance, a…

Machine Learning · Computer Science 2021-02-11 Yikai Zhang , Wenjia Zhang , Sammy Bald , Vamsi Pingali , Chao Chen , Mayank Goswami

Large annotated datasets inevitably contain noisy labels, which poses a major challenge for training deep neural networks as they easily memorize the labels. Noise-robust loss functions have emerged as a notable strategy to counteract this…

Machine Learning · Computer Science 2025-01-28 Max Staats , Matthias Thamm , Bernd Rosenow

Numerous deep learning applications benefit from multi-task learning with multiple regression and classification objectives. In this paper we make the observation that the performance of such systems is strongly dependent on the relative…

Computer Vision and Pattern Recognition · Computer Science 2018-04-25 Alex Kendall , Yarin Gal , Roberto Cipolla

This work primarily focuses on an operator inference methodology aimed at constructing low-dimensional dynamical models based on a priori hypotheses about their structure, often informed by established physics or expert insights. Stability…

Machine Learning · Computer Science 2024-03-04 Igor Pontes Duff , Pawan Goyal , Peter Benner

Markedly increased computational power and data acquisition have led to growing interest in data-driven inverse dynamics problems. These seek to answer a fundamental question: What can we learn from time series measurements of a complex…

Statistical Mechanics · Physics 2025-04-29 Jinghao Lyu , Kyle J. Ray , James P. Crutchfield

Learning with noisy labels is a common challenge in supervised learning. Existing approaches often require practitioners to specify noise rates, i.e., a set of parameters controlling the severity of label noises in the problem, and the…

Machine Learning · Computer Science 2020-08-18 Yang Liu , Hongyi Guo

Many real-world optimization problems contain parameters that are unknown before deployment time, either due to stochasticity or to lack of information (e.g., demand or travel times in delivery problems). A common strategy in such cases is…

It seems that in the current age, computers, computation, and data have an increasingly important role to play in scientific research and discovery. This is reflected in part by the rise of machine learning and artificial intelligence,…

Machine Learning · Computer Science 2024-05-15 Ronan Keane