Related papers: Error Approximation and Bias Correction in Dynamic…

A neural network is essentially a high-dimensional complex mapping model by adjusting network weights for feature fitting. However, the spectral bias in network training leads to unbearable training epochs for fitting the high-frequency…

This study explores the development of a hybrid deep convolutional neural network (DCNN) model enhanced by autoencoders and data augmentation techniques to predict critical heat flux (CHF) with high accuracy. By augmenting the original…

Highly accurate numerical or physical experiments are often time-consuming or expensive to obtain. When time or budget restrictions prohibit the generation of additional data, the amount of available samples may be too limited to provide…

Short-term load forecasting (STLF) is challenging due to complex time series (TS) which express three seasonal patterns and a nonlinear trend. This paper proposes a novel hybrid hierarchical deep learning model that deals with multiple…

Financial fraud detection remains a critical challenge due to the dynamic and adversarial nature of fraudulent behavior. As fraudsters evolve their tactics, detection systems must combine robustness, adaptability, and precision. This study…

Large-scale optimization problems are ubiquitous in the physical sciences; yet, high-fidelity models can often be complex and computationally prohibitive for optimization. A practical alternative is to use a low-fidelity model to facilitate…

Simulating complex unsteady physical phenomena relies on detailed mathematical models, simulated for instance by using the Finite Element Method (FEM). However, these models often exhibit discrepancies from the reality due to unmodeled…

The accurate and efficient prediction of crack propagation in dielectric materials is a critical challenge in structural health monitoring and the design of smart systems. This work presents a hybrid modeling framework that combines an…

The challenges in feature selection, particularly in balancing model accuracy, interpretability, and computational efficiency, remain a critical issue in advancing machine learning methodologies. To address these complexities, this study…

This paper investigates a novel finite-time gradient descent-based adaptive neural network finite-time control strategy for the attitude tracking of a 3-DOF lab helicopter platform subject to composite disturbances. First, the radial basis…

A multi-fidelity regression model is proposed for combining multiple datasets with different fidelities, particularly abundant low-fidelity data and scarce high-fidelity observations. The model builds upon recent multi-fidelity frameworks…

In this work, we present a hybrid numerical method for solving evolution partial differential equations (PDEs) by merging the time finite element method with deep neural networks. In contrast to the conventional deep learning-based…

We propose a new class of Bayesian neural networks (BNNs) that can be trained using noisy data of variable fidelity, and we apply them to learn function approximations as well as to solve inverse problems based on partial differential…

Models play an essential role in the design process of cyber-physical systems. They form the basis for simulation and analysis and help in identifying design problems as early as possible. However, the construction of models that comprise…

Uncertainties in a structure is inevitable, which generally lead to variation in dynamic response predictions. For a complex structure, brute force Monte Carlo simulation for response variation analysis is infeasible since one single run…

We introduce a method that combines neural operators, physics-informed machine learning, and standard numerical methods for solving PDEs. The proposed approach extends each of the aforementioned methods and unifies them within a single…

The development of data-informed predictive models for dynamical systems is of widespread interest in many disciplines. We present a unifying framework for blending mechanistic and machine-learning approaches to identify dynamical systems…

Solving unsteady partial differential equations (PDEs) using recurrent neural networks (RNNs) typically requires numerical derivatives between each block of the RNN to form the physics informed loss function. However, this introduces the…

In this paper, we provide a theoretical analysis of a type of operator learning method without data reliance based on the classical finite element approximation, which is called the finite element operator network (FEONet). We first…

We show how to construct the deep neural network (DNN) expert to predict quasi-optimal $hp$-refinements for a given computational problem. The main idea is to train the DNN expert during executing the self-adaptive $hp$-finite element…