Related papers: Poseidon: Efficient Foundation Models for PDEs
Physics-based simulations are often used to model and understand complex physical systems and processes in domains like fluid dynamics. Such simulations, although used frequently, have many limitations which could arise either due to the…
Fast and accurate data-driven prediction of molecular properties is pivotal to scientific advancements across myriad chemical domains. Deep learning methods have recently garnered much attention, despite their inability to outperform…
We introduce MORPH, a modality-agnostic, autoregressive foundation model for partial differential equations (PDEs). MORPH is built on a convolutional vision transformer backbone that seamlessly handles heterogeneous spatiotemporal datasets…
Existing architectures for operator learning require that the number and locations of sensors (where the input functions are evaluated) remain the same across all training and test samples, significantly restricting the range of their…
In recent years, applying deep learning to solve physics problems has attracted much attention. Data-driven deep learning methods produce fast numerical operators that can learn approximate solutions to the whole system of partial…
With the rise of powerful foundation models, a pre-training-fine-tuning paradigm becomes increasingly popular these days: A foundation model is pre-trained using a huge amount of data from various sources, and then the downstream users only…
Modern power systems require fast and accurate dynamic simulations for stability assessment, digital twins, and real-time control, but classical ODE solvers are often too slow for large-scale or online applications. We propose a…
Deep operator networks (DeepONet) and neural operators have gained significant attention for their ability to map infinite-dimensional function spaces and perform zero-shot super-resolution. However, these models often require large…
The solution of a PDE over varying initial/boundary conditions on multiple domains is needed in a wide variety of applications, but it is computationally expensive if the solution is computed de novo whenever the initial/boundary conditions…
In this paper, we propose a data-driven model reduction method to solve parabolic inverse source problems efficiently. Our method consists of offline and online stages. In the off-line stage, we explore the low-dimensional structures in the…
Fast and accurate surrogates for physics-driven partial differential equations (PDEs) are essential in fields such as aerodynamics, porous media design, and flow control. However, many transformer-based models and existing neural operators…
Traditional approaches to stabilizing hyperbolic PDEs, such as PDE backstepping, often encounter challenges when dealing with high-dimensional or complex nonlinear problems. Their solutions require high computational and analytical costs.…
World models learn to predict future states of an environment, enabling planning and mental simulation. Current approaches default to Transformer-based predictors operating in learned latent spaces. This comes at a cost: O(N^2) computation…
The neural ordinary differential equation (ODE) framework has emerged as a powerful tool for developing accelerated surrogate models of complex physical systems governed by partial differential equations (PDEs). A popular approach for PDE…
Recent progress in motion forecasting has been substantially driven by self-supervised pre-training. However, adapting pre-trained models for specific downstream tasks, especially motion prediction, through extensive fine-tuning is often…
Modeling nonlinear spatiotemporal dynamical systems has primarily relied on partial differential equations (PDEs). However, the explicit formulation of PDEs for many underexplored processes, such as climate systems, biochemical reaction and…
Floorplanning is the first stage of VLSI physical design. An effective floorplanning engine definitely has positive impact on chip design speed, quality and performance. In this paper, we present a novel mathematical model to characterize…
Physics-informed Machine Learning has recently become attractive for learning physical parameters and features from simulation and observation data. However, most existing methods do not ensure that the physics, such as balance laws (e.g.,…
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…
Can we build a single large model for a wide range of PDE-related scientific learning tasks? Can this model generalize to new PDEs, even of new forms, without any fine-tuning? In-context operator learning and the corresponding model…