Related papers: Similarity-Based Equational Inference in Physics

Statistical (machine learning) tools for equation discovery require large amounts of data that are typically computer generated rather than experimentally observed. Multiscale modeling and stochastic simulations are two areas where learning…

Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in…

Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…

Computational physics increasingly depends on large simulation datasets generated by software that remains under active development for many years. In such settings, reproducibility requires not only well documented data but also explicit…

Calculating the inverse kinematics (IK) is a fundamental challenge in robotics. Compared to numerical or learning-based approaches, analytical IK provides higher efficiency and accuracy. However, existing analytical approaches are difficult…

Synthesizing programs from examples requires searching over a vast, combinatorial space of possible programs. In this search process, a key challenge is representing the behavior of a partially written program before it can be executed, to…

Reinforcement learning has shown great potential in solving complex tasks when large amounts of data can be generated with little effort. In robotics, one approach to generate training data builds on simulations based on dynamics models…

The modern machine learning methods allow one to obtain the data-driven models in various ways. However, the more complex the model is, the harder it is to interpret. In the paper, we describe the algorithm for the mathematical equations…

In view of the paradigm shift that makes science ever more data-driven, in this thesis we propose a synthesis method for encoding and managing large-scale deterministic scientific hypotheses as uncertain and probabilistic data. In the form…

Estimation and inference in dynamic discrete choice models often relies on approximation to lower the computational burden of dynamic programming. Unfortunately, the use of approximation can impart substantial bias in estimation and results…

This research focuses on an innovative task of extracting equations from incomplete data, moving away from traditional methods used for complete solutions. The study addresses the challenge of extracting equations from data, particularly in…

A computational procedure is developed for the efficient calculation of derivatives of integrals over non-separable Gaussian-type basis functions, used for the evaluation of gradients of the total energy in quantum-mechanical simulations.…

We present a differentiable soft-body physics simulator that can be composed with neural networks as a differentiable layer. In contrast to other differentiable physics approaches that use explicit forward models to define state…

Atomistic simulations are widely used to investigate reactive processes but are often limited by the rare event problem due to kinetic bottlenecks. We recently introduced an enhanced sampling approach based on the committor function,…

In a small-step semantics with a deterministic reduction strategy, refocusing is a transformation that connects a reduction-based normalization function (i.e., a normalization function that enumerates the successive terms in a reduction…

As data-driven modeling of physical dynamical systems becomes more prevalent, a new challenge is emerging: making these models more compatible and aligned with existing human knowledge. AI-driven scientific modeling processes typically…

Machine-learning methods are gradually being adopted in a wide variety of social, economic, and scientific contexts, yet they are notorious for struggling with exact mathematics. A typical example is computer algebra, which includes tasks…

Generating dense physical fields from sparse measurements is a fundamental question in sampling, signal processing, and many other applications. State-of-the-art methods either use spatial statistics or rely on examples of dense fields in…

The replicator equation is interpreted as a continuous inference equation and a formal similarity between the discrete replicator equation and Bayesian inference is described. Further connections between inference and the replicator…

Multi-dimensional distributions of discrete data that resemble ellipsoids arise in numerous areas of science, statistics, and computational geometry. We describe a complete algebraic algorithm to determine the quadratic form specifying the…