Variational multiscale reinforcement learning for discovering reduced order closure models of nonlinear spatiotemporal transport systems

• URL: http://arxiv.org/abs/2207.12854v1
• Date: Thu, 7 Jul 2022 19:58:47 GMT
• Title: Variational multiscale reinforcement learning for discovering reduced order closure models of nonlinear spatiotemporal transport systems
• Authors: Omer San, Suraj Pawar, Adil Rasheed
• Abstract summary: Closure models are common in many nonlinear dynamical systems to account for losses due to reduced order representations. In this study, we put forth modular dynamic closure modeling and discovery framework to stabilize Galerkin projection based reduced order models. First, we introduce a multi-modal RL (MMRL) to discover mode-dependant closure policies. We then formulate a variational multiscale RL (VMRL) approach to discover closure models without requiring access to the high fidelity data in designing the reward function.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A central challenge in the computational modeling and simulation of a multitude of science applications is to achieve robust and accurate closures for their coarse-grained representations due to underlying highly nonlinear multiscale interactions. These closure models are common in many nonlinear spatiotemporal systems to account for losses due to reduced order representations, including many transport phenomena in fluids. Previous data-driven closure modeling efforts have mostly focused on supervised learning approaches using high fidelity simulation data. On the other hand, reinforcement learning (RL) is a powerful yet relatively uncharted method in spatiotemporally extended systems. In this study, we put forth a modular dynamic closure modeling and discovery framework to stabilize the Galerkin projection based reduced order models that may arise in many nonlinear spatiotemporal dynamical systems with quadratic nonlinearity. However, a key element in creating a robust RL agent is to introduce a feasible reward function, which can be constituted of any difference metrics between the RL model and high fidelity simulation data. First, we introduce a multi-modal RL (MMRL) to discover mode-dependant closure policies that utilize the high fidelity data in rewarding our RL agent. We then formulate a variational multiscale RL (VMRL) approach to discover closure models without requiring access to the high fidelity data in designing the reward function. Specifically, our chief innovation is to leverage variational multiscale formalism to quantify the difference between modal interactions in Galerkin systems. Our results in simulating the viscous Burgers equation indicate that the proposed VMRL method leads to robust and accurate closure parameterizations, and it may potentially be used to discover scale-aware closure models for complex dynamical systems.

Related papers

• SMILE: Zero-Shot Sparse Mixture of Low-Rank Experts Construction From Pre-Trained Foundation Models [85.67096251281191]
  We present an innovative approach to model fusion called zero-shot Sparse MIxture of Low-rank Experts (SMILE) construction. SMILE allows for the upscaling of source models into an MoE model without extra data or further training. We conduct extensive experiments across diverse scenarios, such as image classification and text generation tasks, using full fine-tuning and LoRA fine-tuning.
  arXiv  Detail & Related papers  (2024-08-19T17:32:15Z)
• Data-Driven Stochastic Closure Modeling via Conditional Diffusion Model and Neural Operator [0.0]
  Closure models are widely used in simulating complex multiscale dynamical systems such as turbulence and the earth system. For systems without a clear scale, generalization deterministic and local closure models often lack enough capability. We propose a datadriven modeling framework for constructing neural operator and non-local closure models.
  arXiv  Detail & Related papers  (2024-08-06T05:21:31Z)
• Learning a model is paramount for sample efficiency in reinforcement learning control of PDEs [5.488334211013093]
  We show that learning an actuated model in parallel to training the RL agent significantly reduces the total amount of required data sampled from the real system. We also show that iteratively updating the model is of major importance to avoid biases in the RL training.
  arXiv  Detail & Related papers  (2023-02-14T16:14:39Z)
• Data-driven Control of Agent-based Models: an Equation/Variable-free Machine Learning Approach [0.0]
  We present an Equation/Variable free machine learning (EVFML) framework for the control of the collective dynamics of complex/multiscale systems. The proposed implementation consists of three steps: (A) from high-dimensional agent-based simulations, machine learning (in particular, non-linear manifold learning (DMs)) We exploit the Equation-free approach to perform numerical bifurcation analysis of the emergent dynamics. We design data-driven embedded wash-out controllers that drive the agent-based simulators to their intrinsic, imprecisely known, emergent open-loop unstable steady-states.
  arXiv  Detail & Related papers  (2022-07-12T18:16:22Z)
• Multi-fidelity Hierarchical Neural Processes [79.0284780825048]
  Multi-fidelity surrogate modeling reduces the computational cost by fusing different simulation outputs. We propose Multi-fidelity Hierarchical Neural Processes (MF-HNP), a unified neural latent variable model for multi-fidelity surrogate modeling. We evaluate MF-HNP on epidemiology and climate modeling tasks, achieving competitive performance in terms of accuracy and uncertainty estimation.
  arXiv  Detail & Related papers  (2022-06-10T04:54:13Z)
• Using scientific machine learning for experimental bifurcation analysis of dynamic systems [2.204918347869259]
  This study focuses on training universal differential equation (UDE) models for physical nonlinear dynamical systems with limit cycles. We consider examples where training data is generated by numerical simulations, whereas we also employ the proposed modelling concept to physical experiments. We use both neural networks and Gaussian processes as universal approximators alongside the mechanistic models to give a critical assessment of the accuracy and robustness of the UDE modelling approach.
  arXiv  Detail & Related papers  (2021-10-22T15:43:03Z)
• Closed-form Continuous-Depth Models [99.40335716948101]
  Continuous-depth neural models rely on advanced numerical differential equation solvers. We present a new family of models, termed Closed-form Continuous-depth (CfC) networks, that are simple to describe and at least one order of magnitude faster.
  arXiv  Detail & Related papers  (2021-06-25T22:08:51Z)
• Reinforcement Learning as One Big Sequence Modeling Problem [84.84564880157149]
  Reinforcement learning (RL) is typically concerned with estimating single-step policies or single-step models. We view RL as a sequence modeling problem, with the goal being to predict a sequence of actions that leads to a sequence of high rewards.
  arXiv  Detail & Related papers  (2021-06-03T17:58:51Z)
• Neural Closure Models for Dynamical Systems [35.000303827255024]
  We develop a novel methodology to learn non-Markovian closure parameterizations for low-fidelity models. New "neural closure models" augment low-fidelity models with neural delay differential equations (nDDEs) We show that using non-Markovian over Markovian closures improves long-term accuracy and requires smaller networks.
  arXiv  Detail & Related papers  (2020-12-27T05:55:33Z)
• Improving the Reconstruction of Disentangled Representation Learners via Multi-Stage Modeling [54.94763543386523]
  Current autoencoder-based disentangled representation learning methods achieve disentanglement by penalizing the ( aggregate) posterior to encourage statistical independence of the latent factors. We present a novel multi-stage modeling approach where the disentangled factors are first learned using a penalty-based disentangled representation learning method. Then, the low-quality reconstruction is improved with another deep generative model that is trained to model the missing correlated latent variables.
  arXiv  Detail & Related papers  (2020-10-25T18:51:15Z)
• Kernel and Rich Regimes in Overparametrized Models [69.40899443842443]
  We show that gradient descent on overparametrized multilayer networks can induce rich implicit biases that are not RKHS norms. We also demonstrate this transition empirically for more complex matrix factorization models and multilayer non-linear networks.
  arXiv  Detail & Related papers  (2020-02-20T15:43:02Z)

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.