Related papers: Deep Learning with Physics Priors as Generalized R…

Long scan duration remains a challenge for high-resolution MRI. Deep learning has emerged as a powerful means for accelerated MRI reconstruction by providing data-driven regularizers that are directly learned from data. These data-driven…

Nuclear-norm regularization plays a vital role in many learning tasks, such as low-rank matrix recovery (MR), and low-rank representation (LRR). Solving this problem directly can be computationally expensive due to the unknown rank of…

Accurately predicting fluid dynamics and evolution has been a long-standing challenge in physical sciences. Conventional deep learning methods often rely on the nonlinear modeling capabilities of neural networks to establish mappings…

Neural networks have emerged as effective tools for solving ill-posed inverse problems. In many scientific applications, however, observational training data are insufficient, and learned inverse operators must instead be trained on…

Physics-informed deep learning has achieved remarkable progress by embedding geometric priors, such as Hamiltonian symmetries and variational principles, into neural networks, enabling structure-preserving models that extrapolate with high…

In the past decades, Computed Tomography (CT) has established itself as one of the most important imaging techniques in medicine. Today, the applicability of CT is only limited by the deposited radiation dose, reduction of which manifests…

In this paper we explore the relation between distributionally robust learning and different forms of regularization to enforce robustness of deep neural networks. In particular, starting from a concrete min-max distributionally robust…

Physics-Informed Neural Networks (PINNs) have recently shown great promise as a way of incorporating physics-based domain knowledge, including fundamental governing equations, into neural network models for many complex engineering systems.…

Agents trained with deep reinforcement learning algorithms are capable of performing highly complex tasks including locomotion in continuous environments. We investigate transferring the learning acquired in one task to a set of previously…

This paper deals with the following important research question. Traditionally, the neural network employs non-linear activation functions concatenated with linear operators to approximate a given physical phenomenon. They "fill the space"…

The knowledge that humans hold about a problem often extends far beyond a set of training data and output labels. While the success of deep learning mostly relies on supervised training, important properties cannot be inferred efficiently…

Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…

In machine learning, it is common to optimize the parameters of a probabilistic model, modulated by an ad hoc regularization term that penalizes some values of the parameters. Regularization terms appear naturally in Variational Inference,…

The primary obstacle for applying reinforcement learning (RL) to real-world robotics is the design of effective reward functions. While recently learning-based Process Reward Models (PRMs) are a promising direction, they are often hindered…

In the overview, a generic mathematical object (mapping) is introduced, and its relation to model physics parameterization is explained. Machine learning (ML) tools that can be used to emulate and/or approximate mappings are introduced.…

The large capacity of neural networks enables them to learn complex functions. To avoid overfitting, networks however require a lot of training data that can be expensive and time-consuming to collect. A common practical approach to…

In recent years, pre-trained graph neural networks (GNNs) have been developed as general models which can be effectively fine-tuned for various potential downstream tasks in materials science, and have shown significant improvements in…

Rational approximations are introduced and studied in granular graded rough sets and generalizations thereof by the first author in recent research papers. The concept of rationality is determined by related ontologies and coherence between…

Gradient regularization (GR) has been shown to improve the generalizability of trained models. While Natural Gradient Descent has been shown to accelerate optimization in the initial phase of training, little attention has been paid to how…

During the inversion of discrete linear systems noise in data can be amplified and result in meaningless solutions. To combat this effect, characteristics of solutions that are considered desirable are mathematically implemented during…