Adapting Physics-Informed Neural Networks To Optimize ODEs in Mosquito Population Dynamics
- URL: http://arxiv.org/abs/2406.05108v1
- Date: Fri, 7 Jun 2024 17:40:38 GMT
- Title: Adapting Physics-Informed Neural Networks To Optimize ODEs in Mosquito Population Dynamics
- Authors: Dinh Viet Cuong, Branislava Lalić, Mina Petrić, Binh Nguyen, Mark Roantree,
- Abstract summary: We propose a PINN framework with several improvements for forward and inverse problems for ODE systems.
The framework tackles the gradient imbalance and stiff problems posed by mosquito ordinary differential equations.
Preliminary results indicate that physics-informed machine learning holds significant potential for advancing the study of ecological systems.
- Score: 0.019972837513980313
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Physics informed neural networks have been gaining popularity due to their unique ability to incorporate physics laws into data-driven models, ensuring that the predictions are not only consistent with empirical data but also align with domain-specific knowledge in the form of physics equations. The integration of physics principles enables the method to require less data while maintaining the robustness of deep learning in modeling complex dynamical systems. However, current PINN frameworks are not sufficiently mature for real-world ODE systems, especially those with extreme multi-scale behavior such as mosquito population dynamical modelling. In this research, we propose a PINN framework with several improvements for forward and inverse problems for ODE systems with a case study application in modelling the dynamics of mosquito populations. The framework tackles the gradient imbalance and stiff problems posed by mosquito ordinary differential equations. The method offers a simple but effective way to resolve the time causality issue in PINNs by gradually expanding the training time domain until it covers entire domain of interest. As part of a robust evaluation, we conduct experiments using simulated data to evaluate the effectiveness of the approach. Preliminary results indicate that physics-informed machine learning holds significant potential for advancing the study of ecological systems.
Related papers
- Learning Latent Dynamics via Invariant Decomposition and
(Spatio-)Temporal Transformers [0.6767885381740952]
We propose a method for learning dynamical systems from high-dimensional empirical data.
We focus on the setting in which data are available from multiple different instances of a system.
We study behaviour through simple theoretical analyses and extensive experiments on synthetic and real-world datasets.
arXiv Detail & Related papers (2023-06-21T07:52:07Z) - Learning Neural Constitutive Laws From Motion Observations for
Generalizable PDE Dynamics [97.38308257547186]
Many NN approaches learn an end-to-end model that implicitly models both the governing PDE and material models.
We argue that the governing PDEs are often well-known and should be explicitly enforced rather than learned.
We introduce a new framework termed "Neural Constitutive Laws" (NCLaw) which utilizes a network architecture that strictly guarantees standard priors.
arXiv Detail & Related papers (2023-04-27T17:42:24Z) - MINN: Learning the dynamics of differential-algebraic equations and
application to battery modeling [3.900623554490941]
We propose a novel architecture for generating model-integrated neural networks (MINN)
MINN allows integration on the level of learning physics-based dynamics of the system.
We apply the proposed neural network architecture to model the electrochemical dynamics of lithium-ion batteries.
arXiv Detail & Related papers (2023-04-27T09:11:40Z) - On Robust Numerical Solver for ODE via Self-Attention Mechanism [82.95493796476767]
We explore training efficient and robust AI-enhanced numerical solvers with a small data size by mitigating intrinsic noise disturbances.
We first analyze the ability of the self-attention mechanism to regulate noise in supervised learning and then propose a simple-yet-effective numerical solver, Attr, which introduces an additive self-attention mechanism to the numerical solution of differential equations.
arXiv Detail & Related papers (2023-02-05T01:39:21Z) - EINNs: Epidemiologically-Informed Neural Networks [75.34199997857341]
We introduce a new class of physics-informed neural networks-EINN-crafted for epidemic forecasting.
We investigate how to leverage both the theoretical flexibility provided by mechanistic models as well as the data-driven expressability afforded by AI models.
arXiv Detail & Related papers (2022-02-21T18:59:03Z) - Leveraging the structure of dynamical systems for data-driven modeling [111.45324708884813]
We consider the impact of the training set and its structure on the quality of the long-term prediction.
We show how an informed design of the training set, based on invariants of the system and the structure of the underlying attractor, significantly improves the resulting models.
arXiv Detail & Related papers (2021-12-15T20:09:20Z) - Constructing Neural Network-Based Models for Simulating Dynamical
Systems [59.0861954179401]
Data-driven modeling is an alternative paradigm that seeks to learn an approximation of the dynamics of a system using observations of the true system.
This paper provides a survey of the different ways to construct models of dynamical systems using neural networks.
In addition to the basic overview, we review the related literature and outline the most significant challenges from numerical simulations that this modeling paradigm must overcome.
arXiv Detail & Related papers (2021-11-02T10:51:42Z) - Characterizing possible failure modes in physics-informed neural
networks [55.83255669840384]
Recent work in scientific machine learning has developed so-called physics-informed neural network (PINN) models.
We demonstrate that, while existing PINN methodologies can learn good models for relatively trivial problems, they can easily fail to learn relevant physical phenomena even for simple PDEs.
We show that these possible failure modes are not due to the lack of expressivity in the NN architecture, but that the PINN's setup makes the loss landscape very hard to optimize.
arXiv Detail & Related papers (2021-09-02T16:06:45Z) - Physics-Coupled Spatio-Temporal Active Learning for Dynamical Systems [15.923190628643681]
One of the major challenges is to infer the underlying causes, which generate the perceived data stream.
Success of machine learning based predictive models requires massive annotated data for model training.
Our experiments on both synthetic and real-world datasets exhibit that the proposed ST-PCNN with active learning converges to optimal accuracy with substantially fewer instances.
arXiv Detail & Related papers (2021-08-11T18:05:55Z) - Hard Encoding of Physics for Learning Spatiotemporal Dynamics [8.546520029145853]
We propose a deep learning architecture that forcibly encodes known physics knowledge to facilitate learning in a data-driven manner.
The coercive encoding mechanism of physics, which is fundamentally different from the penalty-based physics-informed learning, ensures the network to rigorously obey given physics.
arXiv Detail & Related papers (2021-05-02T21:40:39Z) - Modeling System Dynamics with Physics-Informed Neural Networks Based on
Lagrangian Mechanics [3.214927790437842]
Two main modeling approaches often fail to meet requirements: first principles methods suffer from high bias, whereas data-driven modeling tends to have high variance.
We present physics-informed neural ordinary differential equations (PINODE), a hybrid model that combines the two modeling techniques to overcome the aforementioned problems.
Our findings are of interest for model-based control and system identification of mechanical systems.
arXiv Detail & Related papers (2020-05-29T15:10:43Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.