Related papers: Towards a Foundation Model for Partial Differentia…
Numerical approximations of partial differential equations (PDEs) are routinely employed to formulate the solution of physics, engineering, and mathematical problems involving functions of several variables, such as the propagation of heat…
Physics-informed deep operator networks (DeepONets) have emerged as a promising approach toward numerically approximating the solution of partial differential equations (PDEs). In this work, we aim to develop further understanding of what…
Diffusion models provide expressive priors for forecasting trajectories of dynamical systems, but are typically unreliable in the sparse data regime. Physics-informed machine learning (PIML) improves reliability in such settings; however,…
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),…
This study proposes FTI-PBSM (Fixed-Time-Increment Physics-informed neural network-Based Surrogate Model), a novel physics-informed surrogate modeling framework designed for real-time reconstruction of transient responses in time-dependent…
Spatio-Temporal (ST) data science, which includes sensing, managing, and mining large-scale data across space and time, is fundamental to understanding complex systems in domains such as urban computing, climate science, and intelligent…
Solving partial differential equations (PDEs) serves as a cornerstone for modeling complex dynamical systems. Recent progresses have demonstrated grand benefits of data-driven neural-based models for predicting spatiotemporal dynamics…
This manuscript reports the first step towards building a robust and efficient model reduction methodology to capture transient dynamics in a transmission level electric power system. Such dynamics is normally modeled on…
Physics-informed neural operators have emerged as a powerful paradigm for solving parametric partial differential equations (PDEs), particularly in the aerospace field, enabling the learning of solution operators that generalize across…
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…
Solving time-dependent Partial Differential Equations (PDEs) using a densely discretized spatial domain is a fundamental problem in various scientific and engineering disciplines, including modeling climate phenomena and fluid dynamics.…
Fractional Differential Equations (FDEs) are essential tools for modelling complex systems in science and engineering. They extend the traditional concepts of differentiation and integration to non-integer orders, enabling a more precise…
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 paper introduces PDEformer, a neural solver for partial differential equations (PDEs) capable of simultaneously addressing various types of PDEs. We propose to represent the PDE in the form of a computational graph, facilitating the…
Traditional radio map estimation (RME) techniques fail to capture multi-dimensional and dynamic characteristics of complex spectrum environments. Recent data-driven methods achieve accurate RME in spatial domain, but ignore physical prior…
We consider solving complex spatiotemporal dynamical systems governed by partial differential equations (PDEs) using frequency domain-based discrete learning approaches, such as Fourier neural operators. Despite their widespread use for…
Modeling complex dynamical systems with only partial knowledge of their physical mechanisms is a crucial problem across all scientific and engineering disciplines. Purely data-driven approaches, which only make use of an artificial neural…
Traditional foundation models are pre-trained on broad datasets to reduce the training resources (e.g., time, energy, labeled samples) needed for fine-tuning a wide range of downstream tasks. However, traditional foundation models struggle…
Equations governing physico-chemical processes are usually known at microscopic spatial scales, yet one suspects that there exist equations, e.g. in the form of Partial Differential Equations (PDEs), that can explain the system evolution at…
There have been growing interests in leveraging experimental measurements to discover the underlying partial differential equations (PDEs) that govern complex physical phenomena. Although past research attempts have achieved great success…