8 papers
Discrete-time dynamics, step-skew products, and pipe-flows
Suddhasattwa Das
Dynamical processes can be classified in various ways as deterministic or stochastic, and continuous or discrete time. All these types can be studied by the path-spaces they genera…
Physics-informed machine learning for reconstruction of dynamical systems with invariant measure score matching
Yongsheng Chen, Suddhasattwa Das, Wei Guo +1
In this paper, we develop a novel mesh-free framework, termed physics-informed neural networks with invariant measure score matching (PINN-IMSM), for reconstructing dynamical syste…
Dynamics, data and reconstruction
Suddhasattwa Das, Tomoharu Suda
The goal of data-driven learning of dynamical systems is to interpret time series as a continuous observation of an underlying dynamical system. This task is not well-posed for a v…
The concept of null in general spaces and contexts
Suddhasattwa Das
The notions of null-sets and nullity are present in all discourses of mathematics. They are based on the dual-pair of notions of "almost-every" and "almost none". A notion of nulli…
A probabilistic approach to drift estimation from stochastic data
Suddhasattwa Das
Timeseries generated from a dynamical source can often be modeled as sample paths of a stochastic differential equation (SDE). The timeseries thus reflects the motion of a particle…
Dynamical systems as enriched functors
Suddhasattwa Das, Tomoharu Suda
This article presents a general description of dynamical systems using the language of enriched functors and enriched natural transformations. This framework is essential to establ…