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

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.

Multi-task Learning for Real-time Autonomous Driving Leveraging Task-adaptive Attention Generator

Real-time processing is crucial in autonomous driving systems due to the imperative of instantaneous decision-making and rapid response. In real-world scenarios, autonomous vehicles are continuously tasked with interpreting their surroundings, analyzing intricate sensor data, and making decisions within split seconds to ensure safety through numerous computer vision tasks. In this paper, we present a new real-time multi-task network adept at three vital autonomous driving tasks: monocular 3D object detection, semantic segmentation, and dense depth estimation. To counter the challenge of negative transfer, which is the prevalent issue in multi-task learning, we introduce a task-adaptive attention generator. This generator is designed to automatically discern interrelations across the three tasks and arrange the task-sharing pattern, all while leveraging the efficiency of the hard-parameter sharing approach. To the best of our knowledge, the proposed model is pioneering in its capability to concurrently handle multiple tasks, notably 3D object detection, while maintaining real-time processing speeds. Our rigorously optimized network, when tested on the Cityscapes-3D datasets, consistently outperforms various baseline models. Moreover, an in-depth ablation study substantiates the efficacy of the methodologies integrated into our framework.

Long-term Time Series Forecasting based on Decomposition and Neural Ordinary Differential Equations

Long-term time series forecasting (LTSF) is a challenging task that has been investigated in various domains such as finance investment, health care, traffic, and weather forecasting. In recent years, Linear-based LTSF models showed better performance, pointing out the problem of Transformer-based approaches causing temporal information loss. However, Linear-based approach has also limitations that the model is too simple to comprehensively exploit the characteristics of the dataset. To solve these limitations, we propose LTSF-DNODE, which applies a model based on linear ordinary differential equations (ODEs) and a time series decomposition method according to data statistical characteristics. We show that LTSF-DNODE outperforms the baselines on various real-world datasets. In addition, for each dataset, we explore the impacts of regularization in the neural ordinary differential equation (NODE) framework.