Yuanyuan Shi

Cheng Deng, Tianhang Zhang, Zhongmou He et al. · meta-ai, mila

Large language models (LLMs) have achieved great success in general domains of natural language processing. In this paper, we bring LLMs to the realm of geoscience with the objective of advancing research and applications in this field. To this end, we present the first-ever LLM in geoscience, K2, alongside a suite of resources developed to further promote LLM research within geoscience. For instance, we have curated the first geoscience instruction tuning dataset, GeoSignal, which aims to align LLM responses to geoscience-related user queries. Additionally, we have established the first geoscience benchmark, GeoBench, to evaluate LLMs in the context of geoscience. In this work, we experiment with a complete recipe to adapt a pre-trained general-domain LLM to the geoscience domain. Specifically, we further train the LLaMA-7B model on 5.5B tokens of geoscience text corpus, including over 1 million pieces of geoscience literature, and utilize GeoSignal's supervised data to fine-tune the model. Moreover, we share a protocol that can efficiently gather domain-specific data and construct domain-supervised data, even in situations where manpower is scarce. Meanwhile, we equip K2 with the abilities of using tools to be a naive geoscience aide. Experiments conducted on the GeoBench demonstrate the effectiveness of our approach and datasets on geoscience knowledge understanding and utilization.We open-source all the training data and K2 model checkpoints at https://github.com/davendw49/k2.

Miroslav Krstic, Luke Bhan, Yuanyuan Shi

Unlike ODEs, whose models involve system matrices and whose controllers involve vector or matrix gains, PDE models involve functions in those roles functional coefficients, dependent on the spatial variables, and gain functions dependent on space as well. The designs of gains for controllers and observers for PDEs, such as PDE backstepping, are mappings of system model functions into gain functions. These infinite dimensional nonlinear operators are given in an implicit form through PDEs, in spatial variables, which need to be solved to determine the gain function for each new functional coefficient of the PDE. The need for solving such PDEs can be eliminated by learning and approximating the said design mapping in the form of a neural operator. Learning the neural operator requires a sufficient number of prior solutions for the design PDEs, offline, as well as the training of the operator. In recent work, we developed the neural operators for PDE backstepping designs for first order hyperbolic PDEs. Here we extend this framework to the more complex class of parabolic PDEs. The key theoretical question is whether the controllers are still stabilizing, and whether the observers are still convergent, if they employ the approximate functional gains generated by the neural operator. We provide affirmative answers to these questions, namely, we prove stability in closed loop under gains produced by neural operators. We illustrate the theoretical results with numerical tests and publish our code on github. The neural operators are three orders of magnitude faster in generating gain functions than PDE solvers for such gain functions. This opens up the opportunity for the use of this neural operator methodology in adaptive control and in gain scheduling control for nonlinear PDEs.

Yuanyuan Shi, Zongyi Li, Huan Yu et al.

State estimation is important for a variety of tasks, from forecasting to substituting for unmeasured states in feedback controllers. Performing real-time state estimation for PDEs using provably and rapidly converging observers, such as those based on PDE backstepping, is computationally expensive and in many cases prohibitive. We propose a framework for accelerating PDE observer computations using learning-based approaches that are much faster while maintaining accuracy. In particular, we employ the recently-developed Fourier Neural Operator (FNO) to learn the functional mapping from the initial observer state and boundary measurements to the state estimate. By employing backstepping observer gains for previously-designed observers with particular convergence rate guarantees, we provide numerical experiments that evaluate the increased computational efficiency gained with FNO. We consider the state estimation for three benchmark PDE examples motivated by applications: first, for a reaction-diffusion (parabolic) PDE whose state is estimated with an exponential rate of convergence; second, for a parabolic PDE with exact prescribed-time estimation; and, third, for a pair of coupled first-order hyperbolic PDEs that modeling traffic flow density and velocity. The ML-accelerated observers trained on simulation data sets for these PDEs achieves up to three orders of magnitude improvement in computational speed compared to classical methods. This demonstrates the attractiveness of the ML-accelerated observers for real-time state estimation and control.

Sahin Lale, Yuanyuan Shi, Guannan Qu et al.

Learning a dynamical system requires stabilizing the unknown dynamics to avoid state blow-ups. However, current reinforcement learning (RL) methods lack stabilization guarantees, which limits their applicability for the control of safety-critical systems. We propose a model-based RL framework with formal stability guarantees, Krasovskii Constrained RL (KCRL), that adopts Krasovskii's family of Lyapunov functions as a stability constraint. The proposed method learns the system dynamics up to a confidence interval using feature representation, e.g. Random Fourier Features. It then solves a constrained policy optimization problem with a stability constraint based on Krasovskii's method using a primal-dual approach to recover a stabilizing policy. We show that KCRL is guaranteed to learn a stabilizing policy in a finite number of interactions with the underlying unknown system. We also derive the sample complexity upper bound for stabilization of unknown nonlinear dynamical systems via the KCRL framework.

Chi Zhang, Yuanyuan Shi, Yize Chen

Recent advancements in reinforcement learning algorithms have opened doors for researchers to operate and optimize building energy management systems autonomously. However, the lack of an easily configurable building dynamical model and energy management task simulation and evaluation platform has arguably slowed the progress in developing advanced and dedicated reinforcement learning (RL) and control algorithms for building operation tasks. Here we propose "BEAR", a physics-principled Building Environment for Control And Reinforcement Learning. The platform allows researchers to benchmark both model-based and model-free controllers using a broad collection of standard building models in Python without co-simulation using external building simulators. In this paper, we discuss the design of this platform and compare it with other existing building simulation frameworks. We demonstrate the compatibility and performance of BEAR with different controllers, including both model predictive control (MPC) and several state-of-the-art RL methods with two case studies.

Ningkun Zheng, Xiaoxiang Liu, Bolun Xu et al.

This paper proposes a novel energy storage price arbitrage algorithm combining supervised learning with dynamic programming. The proposed approach uses a neural network to directly predicts the opportunity cost at different energy storage state-of-charge levels, and then input the predicted opportunity cost into a model-based arbitrage control algorithm for optimal decisions. We generate the historical optimal opportunity value function using price data and a dynamic programming algorithm, then use it as the ground truth and historical price as predictors to train the opportunity value function prediction model. Our method achieves 65% to 90% profit compared to perfect foresight in case studies using different energy storage models and price data from New York State, which significantly outperforms existing model-based and learning-based methods. While guaranteeing high profitability, the algorithm is also light-weighted and can be trained and implemented with minimal computational cost. Our results also show that the learned prediction model has excellent transferability. The prediction model trained using price data from one region also provides good arbitrage results when tested over other regions.

Jie Feng, Wenqi Cui, Jorge Cortés et al.

The increasing integration of renewable energy resources into power grids has led to time-varying system inertia and consequent degradation in frequency dynamics. A promising solution to alleviate performance degradation is using power electronics interfaced energy resources, such as renewable generators and battery energy storage for primary frequency control, by adjusting their power output set-points in response to frequency deviations. However, designing a frequency controller under time-varying inertia is challenging. Specifically, the stability or optimality of controllers designed for time-invariant systems can be compromised once applied to a time-varying system. We model the frequency dynamics under time-varying inertia as a nonlinear switching system, where the frequency dynamics under each mode are described by the nonlinear swing equations and different modes represent different inertia levels. We identify a key controller structure, named Neural Proportional-Integral (Neural-PI) controller, that guarantees exponential input-to-state stability for each mode. To further improve performance, we present an online event-triggered switching algorithm to select the most suitable controller from a set of Neural-PI controllers, each optimized for specific inertia levels. Simulations on the IEEE 39-bus system validate the effectiveness of the proposed online switching control method with stability guarantees and optimized performance for frequency control under time-varying inertia.

Yujia Huang, Ivan Dario Jimenez Rodriguez, Huan Zhang et al.

Forward invariance is a long-studied property in control theory that is used to certify that a dynamical system stays within some pre-specified set of states for all time, and also admits robustness guarantees (e.g., the certificate holds under perturbations). We propose a general framework for training and provably certifying robust forward invariance in Neural ODEs. We apply this framework to provide certified safety in robust continuous control. To our knowledge, this is the first instance of training Neural ODE policies with such non-vacuous certified guarantees. In addition, we explore the generality of our framework by using it to certify adversarial robustness for image classification.

Maxence Lamarque, Luke Bhan, Yuanyuan Shi et al.

To stabilize PDEs, feedback controllers require gain kernel functions, which are themselves governed by PDEs. Furthermore, these gain-kernel PDEs depend on the PDE plants' functional coefficients. The functional coefficients in PDE plants are often unknown. This requires an adaptive approach to PDE control, i.e., an estimation of the plant coefficients conducted concurrently with control, where a separate PDE for the gain kernel must be solved at each timestep upon the update in the plant coefficient function estimate. Solving a PDE at each timestep is computationally expensive and a barrier to the implementation of real-time adaptive control of PDEs. Recently, results in neural operator (NO) approximations of functional mappings have been introduced into PDE control, for replacing the computation of the gain kernel with a neural network that is trained, once offline, and reused in real-time for rapid solution of the PDEs. In this paper, we present the first result on applying NOs in adaptive PDE control, presented for a benchmark 1-D hyperbolic PDE with recirculation. We establish global stabilization via Lyapunov analysis, in the plant and parameter error states, and also present an alternative approach, via passive identifiers, which avoids the strong assumptions on kernel differentiability. We then present numerical simulations demonstrating stability and observe speedups up to three orders of magnitude, highlighting the real-time efficacy of neural operators in adaptive control. Our code (Github) is made publicly available for future researchers.

Luke Bhan, Yuexin Bian, Miroslav Krstic et al.

Over the last decade, data-driven methods have surged in popularity, emerging as valuable tools for control theory. As such, neural network approximations of control feedback laws, system dynamics, and even Lyapunov functions have attracted growing attention. With the ascent of learning based control, the need for accurate, fast, and easy-to-use benchmarks has increased. In this work, we present the first learning-based environment for boundary control of PDEs. In our benchmark, we introduce three foundational PDE problems - a 1D transport PDE, a 1D reaction-diffusion PDE, and a 2D Navier-Stokes PDE - whose solvers are bundled in an user-friendly reinforcement learning gym. With this gym, we then present the first set of model-free, reinforcement learning algorithms for solving this series of benchmark problems, achieving stability, although at a higher cost compared to model-based PDE backstepping. With the set of benchmark environments and detailed examples, this work significantly lowers the barrier to entry for learning-based PDE control - a topic largely unexplored by the data-driven control community. The entire benchmark is available on Github along with detailed documentation and the presented reinforcement learning models are open sourced.

Yihong Guo, Yixuan Wang, Yuanyuan Shi et al.

Training a policy in a source domain for deployment in the target domain under a dynamics shift can be challenging, often resulting in performance degradation. Previous work tackles this challenge by training on the source domain with modified rewards derived by matching distributions between the source and the target optimal trajectories. However, pure modified rewards only ensure the behavior of the learned policy in the source domain resembles trajectories produced by the target optimal policies, which does not guarantee optimal performance when the learned policy is actually deployed to the target domain. In this work, we propose to utilize imitation learning to transfer the policy learned from the reward modification to the target domain so that the new policy can generate the same trajectories in the target domain. Our approach, Domain Adaptation and Reward Augmented Imitation Learning (DARAIL), utilizes the reward modification for domain adaptation and follows the general framework of generative adversarial imitation learning from observation (GAIfO) by applying a reward augmented estimator for the policy optimization step. Theoretically, we present an error bound for our method under a mild assumption regarding the dynamics shift to justify the motivation of our method. Empirically, our method outperforms the pure modified reward method without imitation learning and also outperforms other baselines in benchmark off-dynamics environments.

Yufan Zhang, Honglin Wen, Yuexin Bian et al.

Large penetration of renewable energy sources (RESs) brings huge uncertainty into the electricity markets. The current deterministic clearing approach in the day-ahead (DA) market, where RESs participate based on expected production, has been criticized for causing a lack of coordination between the DA and real-time (RT) markets, leading to high overall operating costs. Previous works indicate that improving day-ahead RES entering quantities can significantly mitigate the drawbacks of deterministic clearing. In this work, we propose using a trained forecasting model, referred to as value-oriented forecasting, to determine RES Improved Entering Quantities (RIEQ) more efficiently during the operational phase. Unlike traditional models that minimize statistical forecasting errors, our approach trains model parameters to minimize the expected overall operating costs across both DA and RT markets. We derive the exact form of the loss function used for training, which becomes piecewise linear when market clearing is modeled by linear programs. Additionally, we provide the analytical gradient of the loss function with respect to the forecast, enabling an efficient training strategy. Numerical studies demonstrate that our forecasts significantly reduce overall operating costs for deterministic market clearing compared to conventional forecasts based on expected RES production.

Luke Bhan, Yuanyuan Shi, Iasson Karafyllis et al.

Observers for PDEs are themselves PDEs. Therefore, producing real time estimates with such observers is computationally burdensome. For both finite-dimensional and ODE systems, moving-horizon estimators (MHE) are operators whose output is the state estimate, while their inputs are the initial state estimate at the beginning of the horizon as well as the measured output and input signals over the moving time horizon. In this paper we introduce MHEs for PDEs which remove the need for a numerical solution of an observer PDE in real time. We accomplish this using the PDE backstepping method which, for certain classes of both hyperbolic and parabolic PDEs, produces moving-horizon state estimates explicitly. Precisely, to explicitly produce the state estimates, we employ a backstepping transformation of a hard-to-solve observer PDE into a target observer PDE, which is explicitly solvable. The MHEs we propose are not new observer designs but simply the explicit MHE realizations, over a moving horizon of arbitrary length, of the existing backstepping observers. Our PDE MHEs lack the optimality of the MHEs that arose as duals of MPC, but they are given explicitly, even for PDEs. In the paper we provide explicit formulae for MHEs for both hyperbolic and parabolic PDEs, as well as simulation results that illustrate theoretically guaranteed convergence of the MHEs.

Filip Bajraktari, Luke Bhan, Miroslav Krstic et al.

In this work, we present the first stability results for approximate predictors in multi-input non-linear systems with distinct actuation delays. We show that if the predictor approximation satisfies a uniform (in time) error bound, semi-global practical stability is correspondingly achieved. For such approximators, the required uniform error bound depends on the desired region of attraction and the number of control inputs in the system. The result is achieved through transforming the delay into a transport PDE and conducting analysis on the coupled ODE-PDE cascade. To highlight the viability of such error bounds, we demonstrate our results on a class of approximators - neural operators - showcasing sufficiency for satisfying such a universal bound both theoretically and in simulation on a mobile robot experiment.