MaD-Scientist: AI-based Scientist solving Convection-Diffusion-Reaction Equations Using Massive PINN-Based Prior Data

• URL: http://arxiv.org/abs/2410.06442v1
• Date: Wed, 9 Oct 2024 00:52:00 GMT
• Title: MaD-Scientist: AI-based Scientist solving Convection-Diffusion-Reaction Equations Using Massive PINN-Based Prior Data
• Authors: Mingu Kang, Dongseok Lee, Woojin Cho, Jaehyeon Park, Kookjin Lee, Anthony Gruber, Youngjoon Hong, Noseong Park,
• Abstract summary: We explore whether a similar approach can be applied to scientific foundation models (SFMs) We collect low-cost physics-informed neural network (PINN)-based approximated prior data in the form of solutions to partial differential equations (PDEs) constructed through an arbitrary linear combination of mathematical dictionaries. We provide experimental evidence on the one-dimensional convection-diffusion-reaction equation, which demonstrate that pre-training remains robust even with approximated prior data.
• Score: 22.262191225577244
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Large language models (LLMs), like ChatGPT, have shown that even trained with noisy prior data, they can generalize effectively to new tasks through in-context learning (ICL) and pre-training techniques. Motivated by this, we explore whether a similar approach can be applied to scientific foundation models (SFMs). Our methodology is structured as follows: (i) we collect low-cost physics-informed neural network (PINN)-based approximated prior data in the form of solutions to partial differential equations (PDEs) constructed through an arbitrary linear combination of mathematical dictionaries; (ii) we utilize Transformer architectures with self and cross-attention mechanisms to predict PDE solutions without knowledge of the governing equations in a zero-shot setting; (iii) we provide experimental evidence on the one-dimensional convection-diffusion-reaction equation, which demonstrate that pre-training remains robust even with approximated prior data, with only marginal impacts on test accuracy. Notably, this finding opens the path to pre-training SFMs with realistic, low-cost data instead of (or in conjunction with) numerical high-cost data. These results support the conjecture that SFMs can improve in a manner similar to LLMs, where fully cleaning the vast set of sentences crawled from the Internet is nearly impossible.

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