Related papers: Learning-based State Reconstruction for a Scalar H…
In principle, the state space of a chaotic attractor can be partially or wholly reconstructed from interspike intervals recorded from experiment. Under certain conditions, the quality of a partial reconstruction, as measured by the spike…
In a more connected world, modeling multi-agent systems with hyperbolic partial differential equations (PDEs) offers a compact, physics-consistent description of collective dynamics. However, classical control tools need adaptation for…
In this paper, we develop a kernel learning backward SDE filter method to estimate the state of a stochastic dynamical system based on its partial noisy observations. A system of forward backward stochastic differential equations is used to…
Obtaining system parameters and reconstructing the full flow state from limited velocity observations using conventional fluid dynamics solvers can be prohibitively expensive. Here we employ machine learning algorithms to overcome the…
Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…
This paper considers the filtering problem which consists in reconstructing the state of a dynamical system with partial observations coming from sensor measurements, and the knowledge that the dynamics are governed by a physical PDE model…
Discrete-time modeling of acoustic, mechanical and electrical systems is a prominent topic in the musical signal processing literature. Such models are mostly derived by discretizing a mathematical model, given in terms of ordinary or…
Common problem in signal processing is reconstruction of the missing signal samples. Missing samples can occur by intentionally omitting signal coefficients to reduce memory requirements, or to speed up the transmission process. Also, noisy…
The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and…
This article investigates the modeling and control of Lagrangian systems involving non-conservative forces using a hybrid method that does not require acceleration calculations. It focuses in particular on the derivation and identification…
We develop an approach to learn an interpretable semi-parametric model of a latent continuous-time stochastic dynamical system, assuming noisy high-dimensional outputs sampled at uneven times. The dynamics are described by a nonlinear…
The image reconstruction of partially coherent light is interpreted as the quantum state reconstruction. The efficient method based on maximum-likelihood estimation is proposed to acquire information from registered intensity measurements…
A new algorithm is presented for reconstructing stochastic nonlinear dynamical models from noisy time-series data. The approach is analytical; consequently, the resulting algorithm does not require an extensive global search for the model…
We present a statistical learning framework for robust identification of partial differential equations from noisy spatiotemporal data. Extending previous sparse regression approaches for inferring PDE models from simulated data, we address…
We consider the problem of real-time reconstruction of urban air pollution maps. The task is challenging due to the heterogeneous sources of available data, the scarcity of direct measurements, the presence of noise, and the large surfaces…
The importance of state estimation in fluid mechanics is well-established; it is required for accomplishing several tasks including design/optimization, active control, and future state prediction. A common tactic in this regards is to rely…
System identification in scenarios where the observed number of variables is less than the degrees of freedom in the dynamics is an important challenge. In this work we tackle this problem by using a recognition network to increase the…
In this paper we explore the performance of deep hidden physics model (M. Raissi 2018) for autonomous systems. These systems are described by set of ordinary differential equations which do not explicitly depend on time. Such systems can be…
We investigate the state space reconstruction from multiple time series derived from continuous and discrete systems and propose a method for building embedding vectors progressively using information measure criteria regarding past,…
Reconstruction fidelity of sparse signals contaminated by sparse noise is considered. Statistical mechanics inspired tools are used to show that the l1-norm based convex optimization algorithm exhibits a phase transition between the…