Related papers: Error Approximation and Bias Correction in Dynamic…

In this paper, we consider the problem of estimating parameters of a linear regression model. Using a hybrid systems framework, a hybrid algorithm is proposed allowing the estimate to converge to the exact value of the unknown parameters in…

Multi-fidelity Reinforcement Learning (RL) frameworks efficiently utilize computational resources by integrating analysis models of varying accuracy and costs. The prevailing methodologies, characterized by transfer learning, human-inspired…

Physics-informed neural networks (PINNs) are capable of finding the solution for a given boundary value problem. We employ several ideas from the finite element method (FEM) to enhance the performance of existing PINNs in engineering…

A common goal throughout science and engineering is to solve optimization problems constrained by computational models. However, in many cases a high-fidelity numerical emulation of systems cannot be optimized due to code complexity and…

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…

Aircraft design optimization traditionally relies on computationally expensive simulation techniques such as Finite Element Method (FEM) and Finite Volume Method (FVM), which, while accurate, can significantly slow down the design iteration…

This paper presents a fast and principled approach for solving the visual anomaly detection and segmentation problem. In this setup, we have access to only anomaly-free training data and want to detect and identify anomalies of an arbitrary…

Deep neural networks often rely on spurious features to make predictions, which makes them brittle under distribution shift and on samples where the spurious correlation does not hold (e.g., minority-group examples). Recent studies have…

For many systems in science and engineering, the governing differential equation is either not known or known in an approximate sense. Analyses and design of such systems are governed by data collected from the field and/or laboratory…

In the present work, we introduce a novel approach to enhance the precision of reduced order models by exploiting a multi-fidelity perspective and DeepONets. Reduced models provide a real-time numerical approximation by simplifying the…

Recently, the use of neural networks to accelerate the solving of partial differential equations (PDEs) has gained significant traction in both academia and industry. However, employing neural networks as standalone surrogate models raises…

We propose a finite-element local basis-based operator learning framework for solving partial differential equations (PDEs). Operator learning aims to approximate mappings from input functions to output functions, where the latter are…

Digital twinning offers a capability of effective real-time monitoring and control, which are vital for cost-intensive experimental facilities, particularly the ones where extreme conditions exist. Sparse experimental measurements collected…

This work introduces an adaptive mesh refinement technique for hierarchical hybrid grids with the goal to reach scalability and maintain excellent performance on massively parallel computer systems. On the block structured hierarchical…

The success of deep learning has inspired recent interests in applying neural networks in statistical inference. In this paper, we investigate the use of deep neural networks for nonparametric regression with measurement errors. We propose…

In this paper, we propose a new short-term load forecasting (STLF) model based on contextually enhanced hybrid and hierarchical architecture combining exponential smoothing (ES) and a recurrent neural network (RNN). The model is composed of…

Deep learning inference that needs to largely take place on the 'edge' is a highly computational and memory intensive workload, making it intractable for low-power, embedded platforms such as mobile nodes and remote security applications.…

Numerical modeling errors are unavoidable in finite element analysis. The presence of model errors inherently reflects both model accuracy and uncertainty. To date there have been few methods for explicitly quantifying errors at points of…

In this paper, based on the combination of finite element mesh and neural network, a novel type of neural network element space and corresponding machine learning method are designed for solving partial differential equations. The…

Anticipating the future actions of a human is a widely studied problem in robotics that requires spatio-temporal reasoning. In this work we propose a deep learning approach for anticipation in sensory-rich robotics applications. We…