An official website of the United States government
Abstract Over the past few decades, several data‐driven methods have been developed for identifying a model that accurately describes the process dynamics. Lately, sparse identification of nonlinear dynamics (SINDy) has delivered promising results for various nonlinear processes. However, at any instance of plant‐model mismatch or process upset, retraining the model using SINDy is computationally expensive and cannot guarantee to catch up with rapidly changing dynamics. Hence, we propose operable adaptive sparse identification of systems (OASIS) framework that extends the capabilities of SINDy for accurate, automatic, and adaptive approximation of process models. First, we use SINDy to obtain multiple models from historical data for varying input settings. Next, using these models and their training data, we build a deep neural network that is incorporated in a model predictive control framework for closed‐loop operation. We demonstrate the OASIS methodology on the identification and control of a continuous stirred tank reactor.
more »
« less
Identification of moment equations via data-driven approaches in nonlinear Schrödinger models
IntroductionThe moment quantities associated with the nonlinear Schrödinger equation offer important insights into the evolution dynamics of such dispersive wave partial differential equation (PDE) models. The effective dynamics of the moment quantities are amenable to both analytical and numerical treatments. MethodsIn this paper, we present a data-driven approach associated with the “Sparse Identification of Nonlinear Dynamics” (SINDy) to capture the evolution behaviors of such moment quantities numerically. Results and DiscussionOur method is applied first to some well-known closed systems of ordinary differential equations (ODEs) which describe the evolution dynamics of relevant moment quantities. Our examples are, progressively, of increasing complexity and our findings explore different choices within the SINDy library. We also consider the potential discovery of coordinate transformations that lead to moment system closure. Finally, we extend considerations to settings where a closed analytical form of the moment dynamics is not available.
more »
« less
- PAR ID:
- 10558610
- Publisher / Repository:
- Frontiers in Photonics
- Date Published:
- Journal Name:
- Frontiers in Photonics
- Volume:
- 5
- ISSN:
- 2673-6853
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Alber, Mark (Ed.)Biological systems exhibit complex dynamics that differential equations can often adeptly represent. Ordinary differential equation models are widespread; until recently their construction has required extensive prior knowledge of the system. Machine learning methods offer alternative means of model construction: differential equation models can be learnt from data via model discovery using sparse identification of nonlinear dynamics (SINDy). However, SINDy struggles with realistic levels of biological noise and is limited in its ability to incorporate prior knowledge of the system. We propose a data-driven framework for model discovery and model selection using hybrid dynamical systems: partial models containing missing terms. Neural networks are used to approximate the unknown dynamics of a system, enabling the denoising of the data while simultaneously learning the latent dynamics. Simulations from the fitted neural network are then used to infer models using sparse regression. We show, via model selection, that model discovery using hybrid dynamical systems outperforms alternative approaches. We find it possible to infer models correctly up to high levels of biological noise of different types. We demonstrate the potential to learn models from sparse, noisy data in application to a canonical cell state transition using data derived from single-cell transcriptomics. Overall, this approach provides a practical framework for model discovery in biology in cases where data are noisy and sparse, of particular utility when the underlying biological mechanisms are partially but incompletely known.more » « less
-
With the computational resources becoming available, data-driven methods have emerged as powerful means for equation discovery and model construction. Sparse regression methods such as SINDy (Sparse Identification for Nonlinear Dynamical Systems) can be used for developing reduced-order models of nonlinear systems. In this study, the authors examine how SINDy can be used for developing low-dimensional models for airfoil systems, which experience unsteady aerodynamic loads and flutter instabilities. For a system of multiple closely spaced airfoil oscillators, analytical models are not readily available to determine flutter instabilities, and one has to take recourse to experimental and numerical means. In this work, as a starting point, data collected through simulations of unsteady aerodynamics of a single airfoil oscillator system are considered and a reduced-order model is constructed based on this data.more » « less
-
Abstract Fractional models and their parameters are sensitive to intrinsic microstructural changes in anomalous materials. We investigate how such physics-informed models propagate the evolving anomalous rheology to the nonlinear dynamics of mechanical systems. In particular, we study the vibration of a fractional, geometrically nonlinear viscoelastic cantilever beam, under base excitation and free vibration, where the viscoelasticity is described by a distributed-order fractional model. We employ Hamilton's principle to obtain the equation of motion with the choice of specific material distribution functions that recover a fractional Kelvin–Voigt viscoelastic model of order α. Through spectral decomposition in space, the resulting time-fractional partial differential equation reduces to a nonlinear time-fractional ordinary differential equation, where the linear counterpart is numerically integrated through a direct L1-difference scheme. We further develop a semi-analytical scheme to solve the nonlinear system through a method of multiple scales, yielding a cubic algebraic equation in terms of the frequency. Our numerical results suggest a set of α-dependent anomalous dynamic qualities, such as far-from-equilibrium power-law decay rates, amplitude super-sensitivity at free vibration, and bifurcation in steady-state amplitude at primary resonance.more » « less
-
Abstract AimDue to the sessile nature of flowering plants, movements to new geographical areas occur mainly during seed dispersal. Frugivores tend to be efficient dispersers because animals move within the boundaries of their preferable niches, so seeds are more likely to be transported to environments that are similar to where the parent plant occurs. However, this efficiency can result in less opportunity for niche shifts over macroevolutionary time, ‘trapping’ plant lineages in particular climatic conditions. Here we test this hypothesis by analysing the role that the interaction with frugivores play in changing dynamics of climatic niche evolution in five clades of flowering plants. LocationGlobal. TaxonThe flowering plant families Apocynaceae, Ericaceae, Melastomataceae, Rosaceae and Solanaceae. MethodsWe model climatic niche evolution as a variable parameter Ornstein–Uhlenbeck process. However, rather than assuming regimes a priori, we use a hidden Markov model (HMM) to infer the complex evolutionary history associated with different modes of seed dispersal. In addition to allowing for a more accurate picture of the regimes, the use of HMMs allows partitioning the variance of climatic niche evolution to include dynamics independent of our focal character. ResultsLineages dispersed by frugivores tend to have warmer and wetter climatic optima and are generally associated with areas where potential for vegetation growth is higher. However, lineages distributed in more mesic habitats, such as rainforests, are generally associated with slower rates of climatic niche evolution regardless of their mode of seed dispersal. Main ConclusionsCharacteristics of the abiotic environment may facilitate the evolution of some types of plant–animal interactions. Association with frugivores is an important modulator of how plants move in space, but its impact on their climatic niche evolution appears to be indirect. Seed dispersal by frugivores may facilitate the establishment of lineages in closed canopy biomes, but the general slower rates of climatic niche evolution in these habitats are possibly related to other general aspects of the ‘mesic syndrome’ rather than the behaviour of the animals that disperse their seeds.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3389/fphot.2024.1444993
