Related papers: Projective Embedding of Dynamical Systems: uniform…

With the advent of Joint Embedding Predictive Architectures (JEPAs), which appear to be more capable than reconstruction-based methods, this paper introduces a novel technique for creating world models using continuous-time dynamic systems…

We prove global convergence of classical projection algorithms for feasibility problems involving union convex sets, which refer to sets expressible as the union of a finite number of closed convex sets. We present a unified strategy for…

We introduce a method-of-lines formulation of the closest point method, a numerical technique for solving partial differential equations (PDEs) defined on surfaces. This is an embedding method, which uses an implicit representation of the…

Position based dynamics is a powerful technique for simulating a variety of materials. Its primary strength is its robustness when run with limited computational budget. We develop a novel approach to address problems with PBD for…

We propose a physics-informed consistency modeling framework for solving partial differential equations (PDEs) via fast, few-step generative inference. We identify a key stability challenge in physics-constrained consistency training, where…

Learning a stable Linear Dynamical System (LDS) from data involves creating models that both minimize reconstruction error and enforce stability of the learned representation. We propose a novel algorithm for learning stable LDSs. Using a…

A dynamical system of points moving along the edges of a graph could be considered as a geometrical discrete dynamical system or as a discrete version of a quantum graph with localized wave packets. We study the set of such systems over…

Ordinary differential equations (ODEs) are the primary means to modelling dynamical systems in many natural and engineering sciences. The number of equations required to describe a system with high heterogeneity limits our capability of…

Dexterous and autonomous robots should be capable of executing elaborated dynamical motions skillfully. Learning techniques may be leveraged to build models of such dynamic skills. To accomplish this, the learning model needs to encode a…

New approaches to the study of stability of solutions of Set Differential Equations (SDEs) based on convex geometry and the theory of mixed volumes were proposed. The stability of the forms of program solutions of linear SDEs with a stable…

The fields of compressed sensing (CS) and matrix completion have shown that high-dimensional signals with sparse or low-rank structure can be effectively projected into a low-dimensional space (for efficient acquisition or processing) when…

We provide an elementary proof of Y. Peres' lemma on the existence in certain dynamical systems of what we term heavy points, points whose ergodic averages consistently dominate the expected value of the ergodic averages. We also derive…

A novel approach for supervised classification is presented which sits at the intersection of machine learning and dynamical systems theory. At variance with other methodologies that employ ordinary differential equations for classification…

We establish sharp well-posedness and approximation estimates for variational saddle point systems at the continuous level. The main results of this note have been known to be true only in the finite dimensional case. Known spectral results…

Classical network embeddings create a low dimensional representation of the learned relationships between features across nodes. Such embeddings are important for tasks such as link prediction and node classification. In the current paper,…

We provide one theorem of spectral equivalence of Koopman operators of an original dynamical system and its reconstructed one through the delay-embedding technique. The theorem is proved for measure-preserving maps (e.g. dynamics on compact…

Random Projection is a foundational research topic that connects a bunch of machine learning algorithms under a similar mathematical basis. It is used to reduce the dimensionality of the dataset by projecting the data points efficiently to…

Dynamic Mode Decomposition (DMD) and its variants, such as extended DMD (EDMD), are broadly used to fit simple linear models to dynamical systems known from observable data. As DMD methods work well in several situations but perform poorly…

The existence of generalized steady states (GSSs) in nonlinear mechanical systems under moderate temporally aperiodic forcing has only been shown recently. Here we derive systematic expansions for such GSSs and construct a numerical…

Stability for dynamic network embeddings ensures that nodes behaving the same at different times receive the same embedding, allowing comparison of nodes in the network across time. We present attributed unfolded adjacency spectral…