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Convolutional Neural Networks (CNNs) excel at image classification but remain vulnerable to common corruptions that humans handle with ease. A key reason for this fragility is their reliance on local texture cues rather than global object…

Randomized neural network (RaNN) methods have been proposed for solving various partial differential equations (PDEs), demonstrating high accuracy and efficiency. However, initializing the fixed parameters remains challenging. Additionally,…

In this contribution, we discuss the construction of Polynomial Chaos surrogates for Monte Carlo radiation transport applications via non-intrusive spectral projection. This contribution focuses on improvements with respect to the approach…

Methods based on polynomial chaos expansion allow to approximate the behavior of systems with uncertain parameters by deterministic dynamics. These methods are used in a wide range of applications, spanning from simulation of uncertain…

Convolutional neural networks (CNNs) are extremely popular and effective for image classification tasks but tend to be overly confident in their predictions. Various works have sought to quantify uncertainty associated with these models,…

Deep neural networks possess strong representational capacity yet remain vulnerable to overfitting, primarily because neurons tend to co-adapt in ways that, while capturing complex and fine-grained feature interactions, also reinforce…

We propose a partial differential-integral equation (PDE) framework for deep neural networks (DNNs) and their associated learning problem by taking the continuum limits of both network width and depth. The proposed model captures the…

The black-box nature of Convolutional Neural Networks (CNNs) and their reliance on large datasets limit their use in complex domains with limited labeled data. Physics-Guided Neural Networks (PGNNs) have emerged to address these limitations…

We propose a novel gray-box modeling algorithm for physical systems governed by stochastic differential equations (SDE). The proposed approach, referred to as the Deep Physics Corrector (DPC), blends approximate physics represented in terms…

Differential equations with random parameters have gained significant prominence in recent years due to their importance in mathematical modelling and data assimilation. In many cases, random ordinary differential equations (RODEs) are…

Recently, the advent of deep learning has spurred interest in the development of physics-informed neural networks (PINN) for efficiently solving partial differential equations (PDEs), particularly in a parametric setting. Among all…

Deep neural networks (DNNs) have become ubiquitous thanks to their remarkable ability to model complex patterns across various domains such as computer vision, speech recognition, robotics, etc. While large DNN models are often more…

A surrogate model approximates a computationally expensive solver. Polynomial Chaos is a method to construct surrogate models by summing combinations of carefully chosen polynomials. The polynomials are chosen to respect the probability…

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…

Graph Neural Networks (GNNs) has been widely used in a variety of fields because of their great potential in representing graph-structured data. However, lacking of rigorous uncertainty estimations limits their application in high-stakes.…

With the rise of deep learning technology in practical applications, Convolutional Neural Networks (CNNs) have been able to assist humans in solving many real-world problems. To enhance the performance of CNNs, numerous network…

We present a novel physics-constrained polynomial chaos expansion as a surrogate modeling method capable of performing both scientific machine learning (SciML) and uncertainty quantification (UQ) tasks. The proposed method possesses a…

Predictive coding (PC) is a biologically plausible alternative to standard backpropagation (BP) that minimises an energy function with respect to network activities before updating weights. Recent work has improved the training stability of…

We propose Deep Companion Learning (DCL), a novel training method for Deep Neural Networks (DNNs) that enhances generalization by penalizing inconsistent model predictions compared to its historical performance. To achieve this, we train a…

The omnipresence of deep learning architectures such as deep convolutional neural networks (CNN)s is fueled by the synergistic combination of ever-increasing labeled datasets and specialized hardware. Despite the indisputable success, the…