Related papers: Prediction of Dynamical Systems by Symbolic Regres…

The study of motion in animals and robots has been aided by insights from geometric mechanics. In friction dominated systems, a mechanical "connection" can provide a high fidelity mechanical model. The connection is a co-vector (Lie…

In this paper, a nonlinear symbolic regression technique using an evolutionary algorithm known as multi-gene genetic programming (MGGP) is applied for a data-driven modelling between the dependent and the independent variables. The…

Generalized Linear Models (GLMs) and Single Index Models (SIMs) provide powerful generalizations of linear regression, where the target variable is assumed to be a (possibly unknown) 1-dimensional function of a linear predictor. In general,…

Generative control policies have recently unlocked major progress in robotics. These methods produce action sequences via diffusion or flow matching, with training data provided by demonstrations. But existing methods come with two key…

Non-linear dynamical systems represent a compact, flexible, and robust tool for reactive motion generation. The effectiveness of dynamical systems relies on their ability to accurately represent stable motions. Several approaches have been…

A powerful approach for understanding neural population dynamics is to extract low-dimensional trajectories from population recordings using dimensionality reduction methods. Current approaches for dimensionality reduction on neural data…

Dynamical sampling deals with signals that evolve in time under the action of a linear operator. The purpose of the present paper is to analyze the performance of the basic dynamical sampling algorithms in the finite dimensional case and…

Symbolic regression (SR) aims to discover concise closed-form mathematical equations from data, a task fundamental to scientific discovery. However, the problem is highly challenging because closed-form equations lie in a complex…

We introduce SymbolFit, a framework that automates parametric modeling by using symbolic regression to perform a machine-search for functions that fit the data while simultaneously providing uncertainty estimates in a single run.…

Signal processing traditionally relies on classical statistical modeling techniques. Such model-based methods utilize mathematical formulations that represent the underlying physics, prior information and additional domain knowledge. Simple…

We propose and study a system whose dynamics are governed by predictions of its future states. General formalism and concrete examples are presented. We find that the dynamical characteristics depend on both how to shape predictions as well…

Automating scientific discovery has been a grand goal of Artificial Intelligence (AI) and will bring tremendous societal impact. Learning symbolic expressions from experimental data is a vital step in AI-driven scientific discovery. Despite…

Big data and large-scale machine learning have had a profound impact on science and engineering, particularly in fields focused on forecasting and prediction. Yet, it is still not clear how we can use the superior pattern matching abilities…

Learning processes by exploiting restricted domain knowledge is an important task across a plethora of scientific areas, with more and more hybrid training methods additively combining data-driven and model-based approaches. Although the…

Accurate predictions and representations of plant growth patterns in simulated and controlled environments are important for addressing various challenges in plant phenomics research. This review explores various works on state-of-the-art…

Correctly capturing the symmetry transformations of data can lead to efficient models with strong generalization capabilities, though methods incorporating symmetries often require prior knowledge. While recent advancements have been made…

Discovering the underlying mathematical expressions describing a dataset is a core challenge for artificial intelligence. This is the problem of $\textit{symbolic regression}$. Despite recent advances in training neural networks to solve…

In the sequential decision making setting, an agent aims to achieve systematic generalization over a large, possibly infinite, set of environments. Such environments are modeled as discrete Markov decision processes with both states and…

This work presents a new methodology to obtain probabilistic interval predictions of a dynamical system. The proposed strategy uses stored past system measurements to estimate the future evolution of the system. The method relies on the use…

Robots that interact with humans in a physical space or application need to think about the person's posture, which typically comes from visual sensors like cameras and infra-red. Artificial intelligence and machine learning algorithms use…