Related papers: PPDONet: Deep Operator Networks for Fast Predictio…
Finite element modeling is a well-established tool for structural analysis, yet modeling complex structures often requires extensive pre-processing, significant analysis effort, and considerable time. This study addresses this challenge by…
Neural network based data-driven operator learning schemes have shown tremendous potential in computational mechanics. DeepONet is one such neural network architecture which has gained widespread appreciation owing to its excellent…
Modern laboratory techniques like ultrafast laser excitation and shock compression can bring matter into highly nonequilibrium states with complex structural transformation, metallization and dissociation dynamics. To understand and model…
Machine learning, especially deep learning is gaining much attention due to the breakthrough performance in various cognitive applications. Recently, neural networks (NN) have been intensively explored to model partial differential…
We propose a new deflation strategy to accelerate the convergence of the preconditioned conjugate gradient(PCG) method for solving parametric large-scale linear systems of equations. Unlike traditional deflation techniques that rely on…
Operator learning for complex nonlinear systems is increasingly common in modeling multi-physics and multi-scale systems. However, training such high-dimensional operators requires a large amount of expensive, high-fidelity data, either…
Deep learning algorithms are growing in popularity in the field of exoplanetary science due to their ability to model highly non-linear relations and solve interesting problems in a data-driven manner. Several works have attempted to…
In numerous contexts, high-resolution solutions to partial differential equations are required to capture faithfully essential dynamics which occur at small spatiotemporal scales, but these solutions can be very difficult and slow to obtain…
Port-Hamiltonian neural networks (pHNNs) are emerging as a powerful modeling tool that integrates physical laws with deep learning techniques. While most research has focused on modeling the entire dynamics of interconnected systems, the…
Phase-field modeling is an effective but computationally expensive method for capturing the mesoscale morphological and microstructure evolution in materials. Hence, fast and generalizable surrogate models are needed to alleviate the cost…
Predicting the evolution of systems that exhibit spatio-temporal dynamics in response to external stimuli is a key enabling technology fostering scientific innovation. Traditional equations-based approaches leverage first principles to…
Deep operator network (DeepONet) has shown significant promise as surrogate models for systems governed by partial differential equations (PDEs), enabling accurate mappings between infinite-dimensional function spaces. However, when applied…
Developing the proper representations for simulating high-speed flows with strong shock waves, rarefactions, and contact discontinuities has been a long-standing question in numerical analysis. Herein, we employ neural operators to solve…
Computing the mass of planetary envelopes and the critical mass beyond which planets accrete gas in a runaway fashion is important when studying planet formation, in particular for planets up to the Neptune mass range. This computation…
The deep operator networks (DeepONet), a class of neural operators that learn mappings between function spaces, have recently been developed as surrogate models for parametric partial differential equations (PDEs). In this work we propose a…
The recently introduced DeepONet operator-learning framework for PDE control is extended from the results for basic hyperbolic and parabolic PDEs to an advanced hyperbolic class that involves delays on both the state and the system output…
The detection of exoplanets with the radial velocity method consists in detecting variations of the stellar velocity caused by an unseen sub-stellar companion. Instrumental errors, irregular time sampling, and different noise sources…
The solution of partial differential equations (PDEs) plays a central role in numerous applications in science and engineering, particularly those involving multiphase flow in porous media. Complex, nonlinear systems govern these problems…
We present $\phi-$DeepONet, a physics-informed neural operator designed to learn mappings between function spaces that may contain discontinuities or exhibit non-smooth behavior. Classical neural operators are based on the universal…
Deep neural networks (DNNs) have achieved the state of the art performance in numerous fields. However, DNNs need high computation times, and people always expect better performance in a lower computation. Therefore, we study the human…