Related papers: Physics-informed Neural Networks for Solving Inver…

We propose a novel approach to model viscoelasticity materials using neural networks, which capture rate-dependent and nonlinear constitutive relations. However, inputs and outputs of the neural networks are not directly observable, and…

Radiation heat transfer in a graded-index medium often suffers accuracy problems due to the gradual changes in the refractive index. The finite element method, meshfree, and other numerical methods often struggle to maintain accuracy when…

Inverse problems in partial differential equations (PDEs) involve estimating the physical parameters of a system from observed spatiotemporal solution fields. Neural networks are well-suited for PDE parameter estimation due to their…

Modern neural networks tend to be overconfident on unseen, noisy or incorrectly labelled data and do not produce meaningful uncertainty measures. Bayesian deep learning aims to address this shortcoming with variational approximations (such…

We propose a first-order stochastic optimization algorithm incorporating adaptive regularization applicable to machine learning problems in deep learning framework. The adaptive regularization is imposed by stochastic process in determining…

We present a novel approach that integrates unfitted finite element methods and neural networks to approximate partial differential equations on complex geometries. Easy-to-generate background meshes (e.g., a simple Cartesian mesh) that cut…

We consider the task of solving generic inverse problems, where one wishes to determine the hidden parameters of a natural system that will give rise to a particular set of measurements. Recently many new approaches based upon deep learning…

Increasing the mini-batch size for stochastic gradient descent offers significant opportunities to reduce wall-clock training time, but there are a variety of theoretical and systems challenges that impede the widespread success of this…

Inverse problems can be described as limited-data problems in which the signal of interest cannot be observed directly. A physics-based forward model that relates the signal with the observations is typically needed. Unfortunately, unknown…

We introduce an algorithm where the individual bits representing the weights of a neural network are learned. This method allows training weights with integer values on arbitrary bit-depths and naturally uncovers sparse networks, without…

This paper investigates both biomechanical-constrained non-rigid medical image registrations and accurate identifications of material properties for soft tissues, using physics-informed neural networks (PINNs). The complex nonlinear…

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…

Recently, with the significant developments in deep learning techniques, solving underdetermined inverse problems has become one of the major concerns in the medical imaging domain. Typical examples include undersampled magnetic resonance…

Non-invasive assessment of the electrical activation pattern can significantly contribute to the diagnosis and treatment of cardiac arrhythmias, due to faster and safer diagnosis, improved surgical planning and easier follow-up. One…

We introduce a novel physics-informed approach for accurately modeling aggregation kinetics which provides a comprehensive solution in a single run by outputting all model parameters simultaneously, a clear advancement over traditional…

The present work investigates the use of physics-informed neural networks (PINNs) for the 3D reconstruction of unsteady gravity currents from limited data. In the PINN context, the flow fields are reconstructed by training a neural network…

Choosing appropriate step sizes is critical for reducing the computational cost of training large-scale neural network models. Mini-batch sub-sampling (MBSS) is often employed for computational tractability. However, MBSS introduces a…

Momentum methods were originally introduced for their superiority to stochastic gradient descent (SGD) in deterministic settings with convex objective functions. However, despite their widespread application to deep neural networks -- a…

Artificial intelligence (AI) empowers innovative diagnostic tools for common diseases, yet its clinical application in skeletal health evaluation is constrained by unsatisfactory accuracy, owing to the inherent porous and poroelastic…

This work applies concepts of artificial neural networks to identify the parameters of a mathematical model based on phase fields for damage and fracture. Damage mechanics is the part of the continuum mechanics that models the effects of…