Related papers: Stable Differentiable Modal Synthesis for Learning…

Modal synthesis methods are a long-standing approach for modelling distributed musical systems. In some cases extensions are possible in order to handle geometric nonlinearities. One such case is the high-amplitude vibration of a string,…

While significant advancements have been made in music generation and differentiable sound synthesis within machine learning and computer audition, the simulation of instrument vibration guided by physical laws has been underexplored. To…

To fully understand, analyze, and determine the behavior of dynamical systems, it is crucial to identify their intrinsic modal coordinates. In nonlinear dynamical systems, this task is challenging as the modal transformation based on the…

Modal methods for simulating vibrations of strings, membranes, and plates are widely used in acoustics and physically informed audio synthesis. However, traditional implementations, particularly for non-linear models like the von K\'arm\'an…

Nonlinear string vibration, in particular the case of nonplanar motion, has been an area of intense study for many years. Numerical simulation methods, essential for the comparison between measured data and theory, have received somewhat…

We present a novel approach for learning nonlinear dynamic models, which leads to a new set of tools capable of solving problems that are otherwise difficult. We provide theory showing this new approach is consistent for models with long…

Non-linear dynamical systems represent a compact, flexible, and robust tool for reactive motion generation. The effectiveness of dynamical systems relies on their ability to accurately represent stable motions. Several approaches have been…

We study the fundamental problem of learning a marginally stable unknown nonlinear dynamical system. We describe an algorithm for this problem, based on the technique of spectral filtering, which learns a mapping from past observations to…

A computational tool for coarse-graining nonlinear systems of ordinary differential equations in time is discussed. Three illustrative model examples are worked out that demonstrate the range of capability of the method. This includes the…

Accurate knowledge of the state variables in a dynamical system is critical for effective control, diagnosis, and supervision, especially when direct measurements of all states are infeasible. This paper presents a novel approach to…

We propose a novel framework for learning stabilizable nonlinear dynamical systems for continuous control tasks in robotics. The key idea is to develop a new control-theoretic regularizer for dynamics fitting rooted in the notion of…

A novel method for the numerical prediction of the slowly varying dynamics of nonlinear mechanical systems has been developed. The method is restricted to the regime of an isolated nonlinear mode and consists of a two-step procedure: In the…

We present a novel method for training score-based generative models which uses nonlinear noising dynamics to improve learning of structured distributions. Generalizing to a nonlinear drift allows for additional structure to be incorporated…

While data-driven model reduction techniques are well-established for linearizable mechanical systems, general approaches to reducing non-linearizable systems with multiple coexisting steady states have been unavailable. In this paper, we…

The objective of this contribution is to compare two methods proposed recently in order to build efficient reduced-order models for geometrically nonlinear structures. The first method relies on the normal form theory that allows one to…

In recent years, a new method for experimental nonlinear modal analysis has been developed, which is based on the extended periodic motion concept. The method is well suited to experimentally obtain amplitude-dependent modal properties…

We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…

Recently there has been substantial interest in spectral methods for learning dynamical systems. These methods are popular since they often offer a good tradeoff between computational and statistical efficiency. Unfortunately, they can be…

A nonlinear partial differential equation is a nonlinear relationship between an unknown function and how it changes due to two or more input variables. A numerical method reduces such an equation to arithmetic for quick visualization, but…

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…