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This paper introduces new parameterizations of equilibrium neural networks, i.e. networks defined by implicit equations. This model class includes standard multilayer and residual networks as special cases. The new parameterization admits a…

Balancing predictive power and interpretability has long been a challenging research area, particularly in powerful yet complex models like neural networks, where nonlinearity obstructs direct interpretation. This paper introduces a novel…

Convex piecewise quadratic (PWQ) functions frequently appear in control and elsewhere. For instance, it is well-known that the optimal value function (OVF) as well as Q-functions for linear MPC are convex PWQ functions. Now, in…

This paper describes and discusses Bayesian Neural Network (BNN). The paper showcases a few different applications of them for classification and regression problems. BNNs are comprised of a Probabilistic Model and a Neural Network. The…

Computational efficiency and robustness are essential in process modeling, optimization, and control for real-world engineering applications. While neural network-based approaches have gained significant attention in recent years,…

Recent breakthroughs in computing power have made it feasible to use machine learning and deep learning to advance scientific computing in many fields, including fluid mechanics, solid mechanics, materials science, etc. Neural networks, in…

Estimating accurate forward and inverse dynamics models is a crucial component of model-based control for sophisticated robots such as robots driven by hydraulics, artificial muscles, or robots dealing with different contact situations.…

Graph neural networks (GNNs) naturally align with sparse operators and unstructured discretizations, making them a promising paradigm for physics-informed machine learning in computational mechanics. Motivated by discrete physics losses and…

There has been an ever-increasing interest in multidisciplinary research on representing and reasoning with imperfect data. Possibilistic networks present one of the powerful frameworks of interest for representing uncertain and imprecise…

The heterogeneous micromechanical properties of biological tissues have profound implications across diverse medical and engineering domains. However, identifying full-field heterogeneous elastic properties of soft materials using…

Hyperbolic spaces, which have the capacity to embed tree structures without distortion owing to their exponential volume growth, have recently been applied to machine learning to better capture the hierarchical nature of data. In this…

Deep generative models are rapidly gaining traction in medical imaging. Nonetheless, most generative architectures struggle to capture the underlying probability distributions of volumetric data, exhibit convergence problems, and offer no…

Neural processes are a family of models which use neural networks to directly parametrise a map from data sets to predictions. Directly parametrising this map enables the use of expressive neural networks in small-data problems where neural…

This work considers artificial feed-forward neural networks as parametric approximators in optimal control of discrete-time systems. Two different approaches are introduced to take polytopic input constraints into account. The first…

This paper proposes a meshless deep learning algorithm, enriched physics-informed neural networks (EPINNs), to solve dynamic Poisson-Nernst-Planck (PNP) equations with strong coupling and nonlinear characteristics. The EPINNs takes the…

Physics Informed Neural Networks offer a mesh free framework for solving PDEs but are highly sensitive to loss weight selection. We propose two dimensional analysis based weighting schemes, one based on quantifiable terms, and another also…

In this paper we present a hybrid neural network augmented physics-based modeling (APBM) framework for Bayesian nonlinear latent space estimation. The proposed APBM strategy allows for model adaptation when new operation conditions come…

Positive systems describing networks with inherently non-negative states and inputs arise naturally in routing, logistics, and compartmental modelling. We consider problems modelled as positive linear systems in incidence form with linear…

A physics-informed neural network (PINN) models the dynamics of a system by integrating the governing physical laws into the architecture of a neural network. By enforcing physical laws as constraints, PINN overcomes challenges with data…

Current deep neural networks are highly overparameterized (up to billions of connection weights) and nonlinear. Yet they can fit data almost perfectly through variants of gradient descent algorithms and achieve unexpected levels of…