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1. Molecular Latent Space Simulators

   https://doi.org/10.1039/D0SC03635H  

   Sidky, Hythem; Chen, Wei; Ferguson, Andrew L (January 2020, Chemical Science)

   Small integration time steps limit molecular dynamics (MD) simulations to millisecond time scales. Markov state models (MSMs) and equation-free approaches learn low-dimensional kinetic models from MD simulation data by performing configurational or dynamical coarse-graining of the state space. The learned kinetic models enable the efficient generation of dynamical trajectories over vastly longer time scales than are accessible by MD, but the discretization of configurational space and/or absence of a means to reconstruct molecular configurations precludes the generation of continuous all-atom molecular trajectories. We propose latent space simulators (LSS) to learn kinetic models for continuous all-atom simulation trajectories by training three deep learning networks to (i) learn the slow collective variables of the molecular system, (ii) propagate the system dynamics within this slow latent space, and (iii) generatively reconstruct molecular configurations. We demonstrate the approach in an application to Trp-cage miniprotein to produce novel ultra-long synthetic folding trajectories that accurately reproduce all-atom molecular structure, thermodynamics, and kinetics at six orders of magnitude lower cost than MD. The dramatically lower cost of trajectory generation enables greatly improved sampling and greatly reduced statistical uncertainties in estimated thermodynamic averages and kinetic rates. 

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2. A Generative Reinforcement Learning Framework for Predictive Analytics

   https://doi.org/10.1109/RAMS51473.2023.10088246  

   Skordilis, Erotokritos; Moghaddass, Ramin; Farhat, Md Tanzin (January 2023, A Generative reinforcement learning framework for predictive analytics)

   In this work, we present a new approach for latent system dynamics and remaining useful life (RUL) estimation of complex degrading systems using generative modeling and reinforcement learning. The main contributions of the proposed method are two-fold. First, we show how a deep generative model can approximate the functionality of high-fidelity simulators and, thus, is able to substitute expensive and complex physics-based models with data-driven surrogate ones. In other words, we can use the generative model in lieu of the actual system as a surrogate model of the system. Furthermore, we show how to use such surrogate models for predictive analytics. Our method follows two main steps. First, we use a deep variational autoencoder (VAE) to learn the distribution over the latent state-space that characterizes the dynamics of the system under monitoring. After model training, the probabilistic VAE decoder becomes the surrogate system model. Then, we develop a scalable reinforcement learning framework using the decoder as the environment, to train an agent for identifying adequate approximate values of the latent dynamics, as well as the RUL. 

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3. Geometric learning for computational mechanics, Part III: Physics-constrained response surface of geometrically nonlinear shells

   https://doi.org/10.1016/j.cma.2023.116219  

   Xiao, Mian; Ma, Ran; Sun, WaiChing (October 2023, Computer Methods in Applied Mechanics and Engineering)

   De Lorenzis, Laura; Papadrakakis, Manolis; Zohdi, Tarek I. (Ed.)

   This paper presents a graph-manifold iterative algorithm to predict the configurations of geometrically exact shells subjected to external loading. The finite element solutions are first stored in a weighted graph where each graph node stores the nodal displacement and nodal director. This collection of solutions is embedded onto a low-dimensional latent space through a graph isomorphism encoder. This graph embedding step reduces the dimensionality of the nonlinear data and makes it easier for the response surface to be constructed. The decoder, in return, converts an element in the latent space back to a weighted graph that represents a finite element solution. As such, the deformed configuration of the shell can be obtained by decoding the predictions in the latent space without running extra finite element simulations. For engineering applications where the shell is often subjected to concentrated loads or a local portion of the shell structure is of particular interest, we use the solutions stored in a graph to reconstruct a smooth manifold where the balance laws are enforced to control the curvature of the shell. The resultant computer algorithm enjoys both the speed of the nonlinear dimensional reduced solver and the fidelity of the solutions at locations where it matters. 

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4. Variational inference with NoFAS: Normalizing flow with adaptive surrogate for computationally expensive models

   https://doi.org/https://doi.org/10.48550/arXiv.2108.12657  

   Wang, Yu; Liu, Fang; Schiavazzi, Daniele E. (October 2022, Journal of computational physics)

   Fast inference of numerical model parameters from data is an important prerequisite to generate predictive models for a wide range of applications. Use of sampling-based approaches such as Markov chain Monte Carlo may become intractable when each likelihood evaluation is computationally expensive. New approaches combining variational inference with normalizing flow are characterized by a computational cost that grows only linearly with the dimensionality of the latent variable space, and rely on gradient-based optimization instead of sampling, providing a more efficient approach for Bayesian inference about the model parameters. Moreover, the cost of frequently evaluating an expensive likelihood can be mitigated by replacing the true model with an offline trained surrogate model, such as neural networks. However, this approach might generate significant bias when the surrogate is insufficiently accurate around the posterior modes. To reduce the computational cost without sacrificing inferential accuracy, we propose Normalizing Flow with Adaptive Surrogate (NoFAS), an optimization strategy that alternatively updates the normalizing flow parameters and surrogate model parameters. We also propose an efficient sample weighting scheme for surrogate model training that preserves global accuracy while effectively capturing high posterior density regions. We demonstrate the inferential and computational superiority of NoFAS against various benchmarks, including cases where the underlying model lacks identifiability. The source code and numerical experiments used for this study are available at https://github.com/cedricwangyu/NoFAS. 

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5. A Generative Reinforcement Learning Framework for Predictive Analytics

   Skordilis, Erotokritos; Moghaddass, Ramin.; Farhat, Tazin. (January 2023, Proceedings annual Reliability and Maintainability Symposium)

   In this work, we present a new approach for latent system dynamics and remaining useful life (RUL) estimation of complex degrading systems using generative modeling and reinforcement learning. The main contributions of the proposed method are two-fold. First, we show how a deep generative model can approximate the functionality of high-fidelity simulators and, thus, is able to substitute expensive and complex physics-based models with data-driven surrogate ones. In other words, we can use the generative model in lieu of the actual system as a surrogate model of the system. Furthermore, we show how to use such surrogate models for predictive analytics. Our method follows two main steps. First, we use a deep variational autoencoder (VAE) to learn the distribution over the latent state-space that characterizes the dynamics of the system under monitoring. After model training, the probabilistic VAE decoder becomes the surrogate system model. Then, we develop a scalable reinforcement learning framework using the decoder as the environment, to train an agent for identifying adequate approximate values of the latent dynamics, as well as the RUL.To our knowledge, the method presented in this paper is the first in industrial prognostics that utilizes generative models and reinforcement learning in that capacity. While the process requires extensive data preprocessing and environment tailored design, which is not always possible, it demonstrates the ability of generative models working in conjunction with reinforcement learning to provide proper value estimations for system dynamics and their RUL. To validate the quality of the proposed method, we conducted numerical experiments using the train_FD002 dataset provided by the NASA CMAPSS data repository. Different subsets were used to train the VAE and the RL agent, and a leftover set was then used for model validation. The results shown prove the merit of our method and will further assist us in developing a data-driven RL environment that incorporates more complex latent dynamic layers, such as normal/faulty operating conditions and hazard processes. 

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