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1. Learning Memory-Based Control for Human-Scale Bipedal Locomotion

   Siekmann, Jonah; Valluri, Srikar; Dao, Jeremy; Bermillo, Lorenzo; Duan, Helei; Fern, Alan; Hurst, Jonathan (January 2020, Robotics science and systems)

   null (Ed.)

   Controlling a non-statically stable biped is a difficult problem largely due to the complex hybrid dynamics involved. Recent work has demonstrated the effectiveness of reinforcement learning (RL) for simulation-based training of neural network controllers that successfully transfer to real bipeds. The existing work, however, has primarily used simple memoryless network architectures, even though more sophisticated architectures, such as those including memory, often yield superior performance in other RL domains. In this work, we consider recurrent neural networks (RNNs) for sim-to-real biped locomotion, allowing for policies that learn to use internal memory to model important physical properties. We show that while RNNs are able to significantly outperform memoryless policies in simulation, they do not exhibit superior behavior on the real biped due to overfitting to the simulation physics unless trained using dynamics randomization to prevent overfitting; this leads to consistently better sim-to-real transfer. We also show that RNNs could use their learned memory states to perform online system identification by encoding parameters of the dynamics into memory. 

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2. Bayesian Recurrent Neural Network Models for Forecasting and Quantifying Uncertainty in Spatial-Temporal Data

   https://doi.org/10.3390/e21020184  

   McDermott, Patrick; Wikle, Christopher (February 2019, Entropy)

   Recurrent neural networks (RNNs) are nonlinear dynamical models commonly used in the machine learning and dynamical systems literature to represent complex dynamical or sequential relationships between variables. Recently, as deep learning models have become more common, RNNs have been used to forecast increasingly complicated systems. Dynamical spatio-temporal processes represent a class of complex systems that can potentially benefit from these types of models. Although the RNN literature is expansive and highly developed, uncertainty quantification is often ignored. Even when considered, the uncertainty is generally quantified without the use of a rigorous framework, such as a fully Bayesian setting. Here we attempt to quantify uncertainty in a more formal framework while maintaining the forecast accuracy that makes these models appealing, by presenting a Bayesian RNN model for nonlinear spatio-temporal forecasting. Additionally, we make simple modifications to the basic RNN to help accommodate the unique nature of nonlinear spatio-temporal data. The proposed model is applied to a Lorenz simulation and two real-world nonlinear spatio-temporal forecasting applications. 

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3. Cross‐Attractor Transforms: Improving Forecasts by Learning Optimal Maps Between Dynamical Systems and Imperfect Models

   https://doi.org/10.1029/2024GL110472  

   Agarwal, N.; Amrhein, D_E; Grooms, I. (February 2025, Geophysical Research Letters)

   Abstract Biased, incomplete numerical models are often used for forecasting states of complex dynamical systems by mapping an estimate of a “true” initial state into model phase space, making a forecast, and then mapping back to the “true” space. While advances have been made to reduce errors associated with model initialization and model forecasts, we lack a general framework for discovering optimal mappings between “true” dynamical systems and model phase spaces. Here, we propose using a data‐driven approach to infer these maps. Our approach consistently reduces errors in the Lorenz‐96 system with an imperfect model constructed to produce significant model errors compared to a reference configuration. Optimal pre‐ and post‐processing transforms leverage “shocks” and “drifts” in the imperfect model to make more skillful forecasts of the reference system. The implemented machine learning architecture using neural networks constructed with a custom analog‐adjoint layer makes the approach generalizable across applications. 

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4. Message Propagation Through Time: An Algorithm for Sequence Dependency Retention in Time Series Modeling

   https://doi.org/10.1137/1.9781611978032.35  

   Xu, Shaoming; Khandelwal, Ankush; Renganathan, Arvind; Kumar, Vipin (April 2024, SIAM International Conference on Data Mining (SDM24))

   Time series modeling, a crucial area in science, often encounters challenges when training Machine Learning (ML) models like Recurrent Neural Networks (RNNs) using the conventional mini-batch training strategy that assumes independent and identically distributed (IID) samples and initializes RNNs with zero hidden states. The IID assumption ignores temporal dependencies among samples, resulting in poor performance. This paper proposes the Message Propagation Through Time (MPTT) algorithm to effectively incorporate long temporal dependencies while preserving faster training times relative to the stateful algorithms. MPTT utilizes two memory modules to asynchronously manage initial hidden states for RNNs, fostering seamless information exchange between samples and allowing diverse mini-batches throughout epochs. MPTT further implements three policies to filter outdated and preserve essential information in the hidden states to generate informative initial hidden states for RNNs, facilitating robust training. Experimental results demonstrate that MPTT outperforms seven strategies on four climate datasets with varying levels of temporal dependencies. 

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5. Machine learning-based statistical closure models for turbulent dynamical systems

   https://doi.org/10.1098/rsta.2021.0205  

   Qi, Di; Harlim, John (August 2022, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences)

   We propose a machine learning (ML) non-Markovian closure modelling framework for accurate predictions of statistical responses of turbulent dynamical systems subjected to external forcings. One of the difficulties in this statistical closure problem is the lack of training data, which is a configuration that is not desirable in supervised learning with neural network models. In this study with the 40-dimensional Lorenz-96 model, the shortage of data is due to the stationarity of the statistics beyond the decorrelation time. Thus, the only informative content in the training data is from the short-time transient statistics. We adopt a unified closure framework on various truncation regimes, including and excluding the detailed dynamical equations for the variances. The closure framework employs a Long-Short-Term-Memory architecture to represent the higher-order unresolved statistical feedbacks with a choice of ansatz that accounts for the intrinsic instability yet produces stable long-time predictions. We found that this unified agnostic ML approach performs well under various truncation scenarios. Numerically, it is shown that the ML closure model can accurately predict the long-time statistical responses subjected to various time-dependent external forces that have larger maximum forcing amplitudes and are not in the training dataset. This article is part of the theme issue ‘Data-driven prediction in dynamical systems’. 

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