Related papers: A Framework for Data-Driven Computational Mechanic…

The principle goal of computational mechanics is to define pattern and structure so that the organization of complex systems can be detected and quantified. Computational mechanics developed from efforts in the 1970s and early 1980s to…

The problem of decomposing non-manifold object has already been studied in solid modeling. However, the few proposed solutions are limited to the problem of decomposing solids described through their boundaries. In this thesis we study the…

We introduce Diffusion Active Learning, a novel approach that combines generative diffusion modeling with data-driven sequential experimental design to adaptively acquire data for inverse problems. Although broadly applicable, we focus on…

This paper proposes a reinforcement learning framework for performance-driven structural design that combines bottom-up design generation with learned strategies to efficiently search large combinatorial design spaces. Motivated by the…

A data-driven formulation of the optimal transport problem is presented and solved using adaptively refined meshes to decompose the problem into a sequence of finite linear programming problems. Both the marginal distributions and their…

With several advantages and as an alternative to predict physics field, machine learning methods can be classified into two distinct types: data-driven relying on training data and physics-driven using physics law. Choosing heat conduction…

Distributed optimization advances centralized machine learning methods by enabling parallel and decentralized learning processes over a network of computing nodes. This work provides an accelerated consensus-based distributed algorithm for…

The task of simultaneously reconstructing multiple physical coefficients in partial differential equations (PDEs) from observed data is ubiquitous in applications. In this work, we propose an integrated data-driven and model-based iterative…

While data-driven methods offer significant promise for modeling complex materials, they often face challenges in generalizing across diverse physical scenarios and maintaining physical consistency. To address these limitations, we propose…

Designing and fabricating structures with specific mechanical properties requires understanding the intricate relationship between design parameters and performance. Understanding the design-performance relationship becomes increasingly…

Accurate models are essential for design, performance prediction, control, and diagnostics in complex engineering systems. Physics-based models excel during the design phase but often become outdated during system deployment due to changing…

Quantum neural networks, parameterized quantum circuits optimized under a specific cost function, provide a paradigm for achieving near-term quantum advantage in quantum information processing. Understanding QNN training dynamics is crucial…

The on-wing engine performance is difficult to track for thermodynamic models because of its inaccurate component maps, and also difficult for data driven methods for their over-fitting to measurement errors. So, we propose a thermodynamic…

Recent advances in machine learning, coupled with low-cost computation, availability of cheap streaming sensors, data storage and cloud technologies, has led to widespread multi-disciplinary research activity with significant interest and…

The application of deep learning toward discovery of data-driven models requires careful application of inductive biases to obtain a description of physics which is both accurate and robust. We present here a framework for discovering…

Data-driven turbulence modeling is a newly emerged research area in thermal hydraulics simulation of nuclear power plant (NPP). The most common CFD method used in NPP thermal hydraulics simulation is Reynolds-averaged Navier-Stokes (RANS)…

Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…

Computational mechanics is a method for discovering, describing and quantifying patterns, using tools from statistical physics. It constructs optimal, minimal models of stochastic processes and their underlying causal structures. These…

For functional data lying on an unknown nonlinear low-dimensional space, we study manifold learning and introduce the notions of manifold mean, manifold modes of functional variation and of functional manifold components. These constitute…

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…