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We propose an evolutionary Multi-objective Optimization for Replica-Exchange-based Physics-informed operator-learning Networks (Morephy-Net) to solve parametric partial differential equations (PDEs) in noisy data regimes, for both forward…

Neural operators extend data-driven models to map between infinite-dimensional functional spaces. While these operators perform effectively in either the time or frequency domain, their performance may be limited when applied to…

We develop and evaluate a method for learning solution operators to nonlinear problems governed by partial differential equations (PDEs). The approach is based on a finite element discretization and aims at representing the solution…

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…

In this paper, we address the issue of modeling and estimating changes in the state of the spatio-temporal dynamical systems based on a sequence of observations like video frames. Traditional numerical simulation systems depend largely on…

Predicting the microstructural and morphological evolution of materials through phase-field modelling is computationally intensive, particularly for high-throughput parametric studies. While neural operators such as the Fourier neural…

Gigantic pre-trained models have become central to natural language processing (NLP), serving as the starting point for fine-tuning towards a range of downstream tasks. However, two pain points persist for this paradigm: (a) as the…

Although very successfully used in conventional machine learning, convolution based neural network architectures -- believed to be inconsistent in function space -- have been largely ignored in the context of learning solution operators of…

Operator learning refers to the application of ideas from machine learning to approximate (typically nonlinear) operators mapping between Banach spaces of functions. Such operators often arise from physical models expressed in terms of…

The operator learning has received significant attention in recent years, with the aim of learning a mapping between function spaces. Prior works have proposed deep neural networks (DNNs) for learning such a mapping, enabling the learning…

Partial-differential-equation (PDE)-constrained optimization is a well-worn technique for acquiring optimal parameters of systems governed by PDEs. However, this approach is limited to providing a single set of optimal parameters per…

Physics-informed neural networks (PINNs) have achieved notable success in modeling dynamical systems governed by partial differential equations (PDEs). To avoid computationally expensive retraining under new physical conditions,…

Neural networks are one tool for approximating non-linear differential equations used in scientific computing tasks such as surrogate modeling, real-time predictions, and optimal control. PDE foundation models utilize neural networks to…

Modeling sequential patterns from data is at the core of various time series forecasting tasks. Deep learning models have greatly outperformed many traditional models, but these black-box models generally lack explainability in prediction…

We propose a trainable-by-parts surrogate model for solving forward and inverse parameterized nonlinear partial differential equations. Like several other surrogate and operator learning models, the proposed approach employs an encoder to…

Design and optimal control problems are among the fundamental, ubiquitous tasks we face in science and engineering. In both cases, we aim to represent and optimize an unknown (black-box) function that associates a performance/outcome to a…

Simulating and controlling physical systems described by partial differential equations (PDEs) are crucial tasks across science and engineering. Recently, diffusion generative models have emerged as a competitive class of methods for these…

Physics-informed neural operators (PINOs) have emerged as powerful tools for learning solution operators of partial differential equations (PDEs). Recent research has demonstrated that incorporating Lie point symmetry information can…

Dynamical systems play a key role in modeling, forecasting, and decision-making across a wide range of scientific domains. However, variations in system parameters, also referred to as parametric variability, can lead to drastically…

Neural operators have achieved strong performance in learning solution operators of partial differential equations (PDEs), but their inherently continuous representations struggle to capture discontinuities and sharp transitions. Existing…