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Algorithms proposed for solving high-dimensional optimization problems with no derivative information frequently encounter the "curse of dimensionality," becoming ineffective as the dimension of the parameter space grows. One feature of a…

Determining the stability of molecules and condensed phases is the cornerstone of atomistic modelling, underpinning our understanding of chemical and materials properties and transformations. Here we show that a machine learning model,…

For various applications, the relations between the dependent and independent variables are highly nonlinear. Consequently, for large scale complex problems, neural networks and regression trees are commonly preferred over linear models…

We show that an optimal finite element mesh refinement algorithm for a prototypical elliptic PDE can be learned by a recurrent neural network with a fixed number of trainable parameters independent of the desired accuracy and the input…

This paper develops a smooth model identification and self-learning strategy for dynamic systems taking into account possible parameter variations and uncertainties. We have tried to solve the problem such that the model follows the changes…

Emulator embedded neural networks, which are a type of physics informed neural network, leverage multi-fidelity data sources for efficient design exploration of aerospace engineering systems. Multiple realizations of the neural network…

We present a novel method for learning reduced-order models of dynamical systems using nonlinear manifolds. First, we learn the manifold by identifying nonlinear structure in the data through a general representation learning problem. The…

Mathematical morphology is a theory and technique to collect features like geometric and topological structures in digital images. Given a target image, determining suitable morphological operations and structuring elements is a cumbersome…

We use a Convolutional Recurrent Neural Network approach to learn morphological evolution driven by surface diffusion. To this aim we first produce a training set using phase field simulations. Intentionally, we insert in such a set only…

Despite recent advances in regularisation theory, the issue of parameter selection still remains a challenge for most applications. In a recent work the framework of statistical learning was used to approximate the optimal Tikhonov…

We explore the use of a topological manifold, represented as a collection of charts, as the target space of neural network based representation learning tasks. This is achieved by a simple adjustment to the output of an encoder's network…

The elastic behavior of materials operating in the linear regime is constrained, by definition, to operations that are linear in the imposed deformation. Though the nonlinear regime holds promise for new functionality, the design in this…

Understanding the learning dynamics and inductive bias of neural networks (NNs) is hindered by the opacity of the relationship between NN parameters and the function represented. We propose reparametrizing ReLU NNs as continuous piecewise…

Normalization Layers (NLs) are widely used in modern deep-learning architectures. Despite their apparent simplicity, their effect on optimization is not yet fully understood. This paper introduces a spherical framework to study the…

Recently developed reduced-order modeling techniques aim to approximate nonlinear dynamical systems on low-dimensional manifolds learned from data. This is an effective approach for modeling dynamics in a post-transient regime where the…

A fundamental property of deep learning normalization techniques, such as batch normalization, is making the pre-normalization parameters scale invariant. The intrinsic domain of such parameters is the unit sphere, and therefore their…

Behavior of neural networks is irremediably determined by the specific loss and data used during training. However it is often desirable to tune the model at inference time based on external factors such as preferences of the user or…

This paper studies the design of neural network (NN)-based controllers for unknown nonlinear systems, using contraction analysis. A Neural Ordinary Differential Equation (NODE) system is constructed by approximating the unknown draft…

To facilitate widespread adoption of automated engineering design techniques, existing methods must become more efficient and generalizable. In the field of topology optimization, this requires the coupling of modern optimization methods…

We apply Physics-Informed Neural Networks (PINNs) for solving identification problems of nonhomogeneous materials. We focus on the problem with a background in elasticity imaging, where one seeks to identify the nonhomogeneous mechanical…