Related papers: Polyconvex anisotropic hyperelasticity with neural…

The requirement of generating predictions that exactly fulfill the fundamental symmetry of the corresponding physical quantities has profoundly shaped the development of machine-learning models for physical simulations. In many cases,…

This paper develops a data-driven safe control framework for nonlinear discrete-time systems with parametric uncertainty and additive disturbances. The proposed approach constructs a data-consistent closed-loop representation that enables…

We present a machine learning framework to train and validate neural networks to predict the anisotropic elastic response of the monoclinic organic molecular crystal $\beta$-HMX in the geometrical nonlinear regime. A filtered molecular…

Representations learnt through deep neural networks tend to be highly informative, but opaque in terms of what information they learn to encode. We introduce an approach to probabilistic modelling that learns to represent data with two…

The joint optimization of the reconstruction and classification error is a hard non convex problem, especially when a non linear mapping is utilized. In order to overcome this obstacle, a novel optimization strategy is proposed, in which a…

The ability to automatically discover interpretable mathematical models from data could forever change how we model soft matter systems. For convex discovery problems with a unique global minimum, model discovery is well-established. It…

The macroscopic response of short fiber reinforced composites is dependent on an extensive range of microstructural parameters. Thus, micromechanical modeling of these materials is challenging and in some cases, computationally expensive.…

We consider uniformly strongly elliptic systems of the second order with bounded coefficients. First, sufficient conditions for the invariance of convex bodies obtained for linear systems without zero order term in bounded domains and…

This paper presents a deep learning based model predictive control algorithm for control affine nonlinear discrete time systems with matched and bounded state dependent uncertainties of unknown structure. Since the structure of…

Neural networks have shown tremendous potential for reconstructing high-resolution images in inverse problems. The non-convex and opaque nature of neural networks, however, hinders their utility in sensitive applications such as medical…

Data-driven models based on deep learning algorithms intend to overcome the limitations of traditional constitutive modelling by directly learning from data. However, the need for extensive data that collate the full state of the material…

As a nonlocal extension of continuum mechanics, peridynamics has been widely and effectively applied in different fields where discontinuities in the field variables arise from an initially continuous body. An important component of the…

We study nonconvex optimization landscapes for learning overcomplete representations, including learning (i) sparsely used overcomplete dictionaries and (ii) convolutional dictionaries, where these unsupervised learning problems find many…

This work presents a two-stage physics-informed, data-driven constitutive modeling framework for hyperelastic soft materials undergoing progressive damage and failure. The framework is grounded in the concept of hyperelasticity with energy…

We present an algorithm for robust model predictive control with consideration of uncertainty and safety constraints. Our framework considers a nonlinear dynamical system subject to disturbances from an unknown but bounded uncertainty set.…

We present a new framework for the simultaneous optimiziation of both the topology as well as the relative density grading of cellular structures and materials, also known as lattices. Due to manufacturing constraints, the optimization…

We propose a neural parameterization of convex sets by learning sublinear (positively homogeneous and convex) functions. Our networks implicitly represent both the support and gauge functions of a convex body. We prove a universal…

The formulation of rheological constitutive equations -- models that relate internal stresses and deformations in complex fluids -- is a critical step in the engineering of systems involving soft materials. While data-driven models provide…

The field of optimal design of linear elastic structures has seen many exciting successes that resulted in new architected materials and structural designs. With the availability of cloud computing, including high-performance computing,…

Data-driven methods have changed the way we understand and model materials. However, while providing unmatched flexibility, these methods have limitations such as reduced capacity to extrapolate, overfitting, and violation of physics…