Related papers: Landau: language for dynamical systems with automa…
Despite the significant strides made by generative AI in just a few short years, its future progress is constrained by the challenge of building modular and robust systems. This capability has been a cornerstone of past technological…
The ever-increasing quantity of multivariate process data is driving a need for skilled engineers to analyze, interpret, and build models from such data. Multivariate data analytics relies heavily on linear algebra, optimization, and…
The use of adaptive workflow management for in situ visualization and analysis has been a growing trend in large-scale scientific simulations. However, coordinating adaptive workflows with traditional procedural programming languages can be…
Classical Bianchi-Lie, Backlund and Darboux transformations are considered. Their generalizations for the dynamical systems are discussed. For the transformation being the generalization of the normal shift the special class of dynamical…
Inspired by the gradient flow viewpoint of the Landau equation and the corresponding dynamic formulation of the Landau metric in [arXiv:2007.08591], we develop a novel implicit particle method for the Landau equation in the framework of the…
The success of large language models (LLMs) depends heavily on large-scale, high-quality instruction-following and reinforcement datasets. However, generating such data through human annotation is prohibitively time-consuming particularly…
We introduce a language for formally reasoning about programs that combine differential constructs with probabilistic ones. The language harbours, for example, such systems as adaptive cruise controllers, continuous-time random walks, and…
Recent work has shown that augmenting environments with language descriptions improves policy learning. However, for environments with complex language abstractions, learning how to ground language to observations is difficult due to…
Many engineering problems involve learning hidden dynamics from indirect observations, where the physical processes are described by systems of partial differential equations (PDE). Gradient-based optimization methods are considered…
Automatic differentiation (AD) is a range of algorithms to compute the numeric value of a function's (partial) derivative, where the function is typically given as a computer program or abstract syntax tree. AD has become immensely popular…
We use a modification of the parameterization method to study invariant manifolds for difference equations. We establish existence, regularity, smooth dependence on parameters and study several singular limits, even if the difference…
We consider forkable regular expressions, which enrich regular expressions with a fork operator, to establish a formal basis for static and dynamic analysis of the communication behavior of concurrent programs. We define a novel…
Spreadsheets provide a flexible and easy to use software development environment, but that leads to error proneness. Work has been done to prevent errors in spreadsheets, including using models to specify distinct parts of a spreadsheet as…
Domain-specific languages (DSLs) for machine learning are revolutionizing the speed and efficiency of machine learning workloads as they enable users easy access to high-performance compiler optimizations and accelerators. However, to take…
The article shows how to learn models of dynamical systems from data which are governed by an unknown variational PDE. Rather than employing reduction techniques, we learn a discrete field theory governed by a discrete Lagrangian density…
Hand-curated natural language systems provide an inspectable, correctable alternative to language systems based on machine learning, but maintaining them requires considerable effort and expertise. Interactive Natural Language Debugging…
Mechanism design has long been a cornerstone of economic theory, with traditional approaches relying on mathematical derivations. Recently, automated approaches, including differentiable economics with neural networks, have emerged for…
Master equations are of fundamental importance in modeling stochastic dynamical systems.However, solving master equations is challenging due to the exponential increase in the number of possible states or trajectories with the dimension of…
Testing autonomous vehicles (AVs) requires complex oracles to determine if the AVs behavior conforms with specifications and humans' expectations. Available open source oracles are tightly embedded in the AV simulation software and are…
Dynamic topological logic ($\mathbf{DTL}$) is a trimodal logic designed for reasoning about dynamic topological systems. It was shown by Fern\'andez-Duque that the natural set of axioms for $\mathbf{DTL}$ is incomplete, but he provided a…