相关论文: Open problems in PDE models for knowledge-based an…

Economists model knowledge use and acquisition as a cause-and-effect calculus associating observations made by a decision-maker about their world with possible underlying causes. Knowledge models are well-established for static contexts,…

To traverse complex three-dimensional terrainwith large obstacles, animals and robots must transition across different modes. However, the most mechanistic understanding of terrestrial locomotion concerns how to generate and stabilize…

A key challenge in off-road navigation is that even visually similar terrains or ones from the same semantic class may have substantially different traction properties. Existing work typically assumes no wheel slip or uses the expected…

Many cognitive neuroscience studies use large feature sets to predict and interpret brain activity patterns. Feature sets take many forms, from human stimulus annotations to representations in deep neural networks. Of crucial importance in…

Over the last decade, data-driven methods have surged in popularity, emerging as valuable tools for control theory. As such, neural network approximations of control feedback laws, system dynamics, and even Lyapunov functions have attracted…

Pedestrian motion prediction is a fundamental task for autonomous robots and vehicles to operate safely. In recent years many complex approaches based on neural networks have been proposed to address this problem. In this work we show that…

In many scientific fields, the generation and evolution of data are governed by partial differential equations (PDEs) which are typically informed by established physical laws at the macroscopic level to describe general and predictable…

Physical reasoning is a core aspect of intelligence in animals and humans. A central question is what model should be used as a basis for reasoning. Existing work considered models ranging from intuitive physics and physical simulators to…

This paper is concerned with mathematical modeling of intelligent systems, such as human crowds and animal groups. In particular, the focus is on the emergence of different self-organized patterns from non-locality and anisotropy of the…

Nature is in constant flux, so animals must account for changes in their environment when making decisions. How animals learn the timescale of such changes and adapt their decision strategies accordingly is not well understood. Recent…

Recent progress in diverse intelligence has shown simple learning capacities below the organism level - single cells and even molecular networks. However, there are still many knowledge gaps around learning capacity above the organism…

Many large scale problems in computational fluid dynamics such as uncertainty quantification, Bayesian inversion, data assimilation and PDE constrained optimization are considered very challenging computationally as they require a large…

Recent advances at the intersection of control theory, neuroscience, and machine learning have revealed novel mechanisms by which dynamical systems perform computation. These advances encompass a wide range of conceptual, mathematical, and…

Animals exploit time to survive in the world. Temporal information is required for higher-level cognitive abilities such as planning, decision making, communication, and effective cooperation. Since time is an inseparable part of cognition,…

We consider the problem of learning the dynamics in the topology of time-evolving point clouds, the prevalent spatiotemporal model for systems exhibiting collective behavior, such as swarms of insects and birds or particles in physics. In…

Wild animals are commonly fitted with trackers that record their position through time, and statistical models for tracking data broadly fall into two categories: models focused on small-scale movement decisions, and models for large-scale…

We propose a neural network based approach for extracting models from dynamic data using ordinary and partial differential equations. In particular, given a time-series or spatio-temporal dataset, we seek to identify an accurate governing…

Modeling complex spatiotemporal dynamical systems, such as the reaction-diffusion processes, have largely relied on partial differential equations (PDEs). However, due to insufficient prior knowledge on some under-explored dynamical…

Understanding how animals learn is a central challenge in neuroscience, with growing relevance to the development of animal- or human-aligned artificial intelligence. However, existing approaches tend to assume fixed parametric forms for…

With the fast and unstoppable evolution of robotics and artificial intelligence, effective autonomous navigation in real-world scenarios has become one of the most pressing challenges in the literature. However, demanding requirements, such…