Related papers: A Unified Data-Driven Framework for Efficient Scie…
The working mechanisms of complex natural systems tend to abide by concise and profound partial differential equations (PDEs). Methods that directly mine equations from data are called PDE discovery, which reveals consistent physical laws…
Complexity science offers a wide range of measures for quantifying unpredictability, structure, and information. Yet, a systematic conceptual organization of these measures is still missing. We present a unified framework that locates…
We perform a full similarity analysis of an idealized ecosystem using Buckingham's $\Pi$ theorem to obtain dimensionless similarity parameters given that some (non- unique) method exists that can differentiate different functional groups of…
The project of physics discovery is often equivalent to finding the most concise description of a physical system. The description with optimum predictive capability for a dataset generated by a physical system is one that minimizes both…
Ongoing efforts that span over decades show a rise of AI methods for accelerating scientific discovery, yet accelerating discovery in mathematics remains a persistent challenge for AI. Specifically, AI methods were not effective in creation…
Fisher information and Shannon entropy are fundamental tools for understanding and analyzing dynamical systems from complementary perspectives. They can characterize unknown parameters by quantifying the information contained in variables,…
Dimensional analysis is one of the most fundamental tools for understanding physical systems. However, the construction of dimensionless variables, as guided by the Buckingham-$\pi$ theorem, is not uniquely determined. Here, we introduce…
Equation discovery is aimed at directly extracting physical laws from data and has emerged as a pivotal research domain. Previous methods based on symbolic mathematics have achieved substantial advancements, but often require the design of…
Symbolic regression plays a crucial role in modern scientific research thanks to its capability of discovering concise and interpretable mathematical expressions from data. A key challenge lies in the search for parsimonious and…
Partial differential equations (PDEs) encode fundamental physical laws, yet closed-form analytical solutions for many important equations remain unknown and typically require substantial human insight to derive. Existing numerical,…
Governing equations are fundamental for describing and predicting dynamic urban geographic systems. Unlike physical systems guided by first principles, urban spatiotemporal phenomena emerge from coupled geographic processes that lack…
Discovering causal direction from temporal observational data is particularly challenging for symbolic sequences, where functional models and noise assumptions are often unavailable. We propose a novel \emph{Dictionary Based Pattern Entropy…
Data science models, although successful in a number of commercial domains, have had limited applicability in scientific problems involving complex physical phenomena. Theory-guided data science (TGDS) is an emerging paradigm that aims to…
Scientific discovery is fundamentally a resource-constrained process that requires navigating complex trade-offs between the quality and quantity of measurements due to physical and cost constraints. Measurements drive the scientific…
Conventional physics-based modeling techniques involve high effort, e.g., time and expert knowledge, while data-driven methods often lack interpretability, structure, and sometimes reliability. To mitigate this, we present a data-driven…
Most research on data discovery has so far focused on improving individual discovery operators such as join, correlation, or union discovery. However, in practice, a combination of these techniques and their corresponding indexes may be…
The ability to discover physical laws and governing equations from data is one of humankind's greatest intellectual achievements. A quantitative understanding of dynamic constraints and balances in nature has facilitated rapid development…
Dynamical systems form the foundation of scientific discovery, traditionally modeled with predefined state variables such as the angle and angular velocity, and differential equations such as the equation of motion for a single pendulum. We…
Many datasets exhibit a well-defined structure that can be exploited to design faster search tools, but it is not always clear when such acceleration is possible. Here, we introduce a framework for similarity search based on characterizing…
Topological phases of matter$\unicode{x2013}$comprising both insulators and semimetals$\unicode{x2013}$offer great potential for quantum applications, but identifying new candidates remains challenging due to expensive first-principles…