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One of the open problems in scientific computing is the long-time integration of nonlinear stochastic partial differential equations (SPDEs). We address this problem by taking advantage of recent advances in scientific machine learning and…
A data-free, predictive scientific AI model, Tensor-decomposition-based A Priori Surrogate (TAPS), is proposed for tackling ultra large-scale engineering simulations with significant speedup, memory savings, and storage gain. TAPS can…
Auto-regressive partial differential equation (PDE) foundation models have shown great potential in handling time-dependent data. However, these models suffer from the shortcut problem deeply rooted in auto-regressive prediction, causing…
Developing accurate, data-efficient surrogate models is central to advancing AI for Science. Neural operators (NOs), which approximate mappings between infinite-dimensional function spaces using conventional neural architectures, have…
The computational resources required to solve the full 3D inversion of time-domain electromagnetic data are immense. To overcome the time-consuming 3D simulations, we construct a surrogate model, more precisely, a data-driven statistical…
Cross-subject electroencephalography (EEG) decoding remains a fundamental challenge in brain-computer interface (BCI) research due to substantial inter-subject variability and the scarcity of subject-invariant representations. This paper…
We introduce a novel grid-independent model for learning partial differential equations (PDEs) from noisy and partial observations on irregular spatiotemporal grids. We propose a space-time continuous latent neural PDE model with an…
Multivariate time series imputation is fundamental in applications such as healthcare, traffic forecasting, and biological modeling, where sensor failures and irregular sampling lead to pervasive missing values. However, existing…
Diffusion-based solvers for partial differential equations (PDEs) are often bottle-necked by slow gradient-based test-time optimization routines that use PDE residuals for loss guidance. They additionally suffer from optimization…
A physics informed neural network (PINN) incorporates the physics of a system by satisfying its boundary value problem through a neural network's loss function. The PINN approach has shown great success in approximating the map between the…
In recent engineering applications using deep learning, physics-informed neural network (PINN) is a new development as it can exploit the underlying physics of engineering systems. The novelty of PINN lies in the use of partial differential…
Parametric surrogate models for partial differential equations (PDEs) are a necessary component for many applications in the computational sciences, and convolutional neural networks (CNNs) have proved as an excellent tool to generate these…
Deep neural networks (DNNs), especially physics-informed neural networks (PINNs), have recently become a new popular method for solving forward and inverse problems governed by partial differential equations (PDEs). However, these methods…
We present a new data-driven reduced-order modeling approach to efficiently solve parametrized partial differential equations (PDEs) for many-query problems. This work is inspired by the concept of implicit neural representation (INR),…
Ultrafast optics is driven by a myriad of complex nonlinear dynamics. The ubiquitous presence of governing equations in the form of partial integro-differential equations (PIDE) necessitates the need for advanced computational tools to…
Physics Informed Neural Networks (PINNs) are shown to be a promising method for the approximation of Partial Differential Equations (PDEs). PINNs approximate the PDE solution by minimizing physics-based loss functions over a given domain.…
Physics-informed neural networks (PINNs) encode physical conservation laws and prior physical knowledge into the neural networks, ensuring the correct physics is represented accurately while alleviating the need for supervised learning to a…
Scientific foundation models are expected to reuse representations under changes in dataset, acquisition protocol, and deployment domain, yet many sequence backbones treat scientific temporal structure as an unconstrained pattern to be…
Recent advancements in deep learning have led to the development of various models for long-term multivariate time-series forecasting (LMTF), many of which have shown promising results. Generally, the focus has been on…
This work is concerned with discovering the governing partial differential equation (PDE) of a physical system. Existing methods have demonstrated the PDE identification from finite observations but failed to maintain satisfying results…