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The black-box nature of neural networks limits the ability to encode or impose specific structural relationships between inputs and outputs. While various studies have introduced architectures that ensure the network's output adheres to a…

Input-convex neural networks (ICNNs) are widely used for log-concave density estimation, convex-potential normalizing flows, optimal transport, and transport-map inversion for high-dimensional Bayesian posteriors. These tasks share a…

Implicit solvent models (ISMs) promise to deliver the accuracy of explicit solvent simulations at a fraction of the computational cost. However, despite decades of development, their accuracy has remained insufficient for many critical…

Input-Convex Neural Networks (ICNNs) are networks that guarantee convexity in their input-output mapping. These networks have been successfully applied for energy-based modelling, optimal transport problems and learning invariances. The…

We propose a multi-scale deep energy model that is strongly convex in the local neighbourhood around the data manifold to represent its probability density, with application in inverse problems. In particular, we represent the negative…

While achieving remarkable success for medical image segmentation, deep convolution neural networks (DCNNs) often fail to maintain their robustness when confronting test data with the novel distribution. To address such a drawback, the…

Supervised convolutional neural networks (CNNs) are widely used to solve imaging inverse problems, achieving state-of-the-art performance in numerous applications. However, despite their empirical success, these methods are poorly…

Despite prior advances in PINNs, significant challenges remain in localized solid mechanics problems because of the limitations of single network formulations in simultaneous resolution of smooth global responses and near-tip singularities,…

Learning time-dependent partial differential equations (PDEs) that govern evolutionary observations is one of the core challenges for data-driven inference in many fields. In this work, we propose to capture the essential dynamics of…

Accurate constitutive models of soft materials are crucial for understanding their mechanical behavior and ensuring reliable predictions in the design process. To this end, scientific machine learning research has produced flexible and…

When the system is linear, why should learning be nonlinear? Linear dynamical systems, the analytical backbone of control theory, signal processing and circuit analysis, have exact closed-form solutions via the state transition matrix. Yet…

In modern computational materials science, deep learning has shown the capability to predict interatomic potentials, thereby supporting and accelerating conventional simulations. However, existing models typically sacrifice either accuracy…

Implicit graph neural networks have gained popularity in recent years as they capture long-range dependencies while improving predictive performance in static graphs. Despite the tussle between performance degradation due to the…

We present a framework for the multiscale modeling of finite strain magneto-elasticity based on physics-augmented neural networks (NNs). By using a set of problem specific invariants as input, an energy functional as the output and by…

In this paper we propose cross-modal convolutional neural networks (X-CNNs), a novel biologically inspired type of CNN architectures, treating gradient descent-specialised CNNs as individual units of processing in a larger-scale network…

Neural networks with ReLU activation function have been shown to be universal function approximators and learn function mapping as non-smooth functions. Recently, there is considerable interest in the use of neural networks in applications…

Despite their great success, there is still no comprehensive theoretical understanding of learning with Deep Neural Networks (DNNs) or their inner organization. Previous work proposed to analyze DNNs in the \textit{Information Plane}; i.e.,…

Geosteering of wells requires fast interpretation of geophysical logs, which is a non-unique inverse problem. Current work presents a proof-of-concept approach to multi-modal probabilistic inversion of logs using a single evaluation of an…

Combining discrete probability distributions and combinatorial optimization problems with neural network components has numerous applications but poses several challenges. We propose Implicit Maximum Likelihood Estimation (I-MLE), a…

This paper presents the input convex neural network architecture. These are scalar-valued (potentially deep) neural networks with constraints on the network parameters such that the output of the network is a convex function of (some of)…