相关论文: MDBench: Benchmarking Data-Driven Methods for Mode…
LLMs are transforming software development, yet current code generation and code repair benchmarks mainly assess syntactic and functional correctness in simple, single-error cases. LLMs' capabilities to autonomously find and fix runtime…
In the last decade, the scientific community has devolved its attention to the deployment of data-driven approaches in scientific research to provide accurate and reliable analysis of a plethora of phenomena. Most notably, Physics-informed…
Partial differential equations (PDEs) govern physical phenomena across the full range of scientific scales, yet their computational solution remains one of the defining challenges of modern science. This critical review examines two mature…
Previous methods evaluate reward models by testing them on a fixed pairwise ranking test set, but they typically do not provide performance information on each preference dimension. In this work, we address the evaluation challenge of…
Given the remarkable performance of Large Language Models (LLMs), an important question arises: Can LLMs conduct human-like scientific research and discover new knowledge, and act as an AI scientist? Scientific discovery is an iterative…
Differential equation discovery, a machine learning subfield, is used to develop interpretable models, particularly in nature-related applications. By expertly incorporating the general parametric form of the equation of motion and…
Many real-world scientific processes are governed by complex nonlinear dynamic systems that can be represented by differential equations. Recently, there has been increased interest in learning, or discovering, the forms of the equations…
Dynamical systems are found in innumerable forms across the physical and biological sciences, yet all these systems fall naturally into universal equivalence classes: conservative or dissipative, stable or unstable, compressible or…
Recent years have witnessed a growth in mathematics for deep learning--which seeks a deeper understanding of the concepts of deep learning with mathematics and explores how to make it more robust--and deep learning for mathematics, where…
Large Atomistic Models (LAMs) have undergone remarkable progress recently, emerging as universal or fundamental representations of the potential energy surface defined by the first-principles calculations of atomistic systems. However, our…
Machine learning based partial differential equations (PDEs) solvers have received great attention in recent years. Most progress in this area has been driven by deep neural networks such as physics-informed neural networks (PINNs) and…
In this paper, we attack the anomaly detection problem by directly modeling the data distribution with deep architectures. We propose deep structured energy based models (DSEBMs), where the energy function is the output of a deterministic…
Recently proposed numerical algorithms for solving high-dimensional nonlinear partial differential equations (PDEs) based on neural networks have shown their remarkable performance. We review some of them and study their convergence…
Benchmark data sets are a cornerstone of machine learning development and applications, ensuring new methods are robust, reliable and competitive. The relative rarity of benchmark sets in computational science, due to the uniqueness of the…
Ordinary differential equations (ODEs) provide a powerful framework for modeling dynamic systems arising in a wide range of scientific domains. However, most existing ODE methods focus on a single system, and do not adequately address the…
Label noise is a common problem in real-world datasets, affecting both model training and validation. Clean data are essential for achieving strong performance and ensuring reliable evaluation. While various techniques have been proposed to…
Signal processing, communications, and control have traditionally relied on classical statistical modeling techniques. Such model-based methods utilize mathematical formulations that represent the underlying physics, prior information and…
Identifying hidden dynamics from observed data is a significant and challenging task in a wide range of applications. Recently, the combination of linear multistep methods (LMMs) and deep learning has been successfully employed to discover…
We introduce and analyze a method of learning-informed parameter identification for partial differential equations (PDEs) in an all-at-once framework. The underlying PDE model is formulated in a rather general setting with three unknowns:…
In the field of machine learning, ensemble learning is widely recognized as a pivotal strategy for pushing the boundaries of predictive performance. Traditional static ensemble methods typically assign weights by treating each base learner…