Draguna Vrabie

A central challenge in the design of energy-efficient wind farms is the presence of wake effects between turbines. When a wind turbine harvests energy from free wind, it produces a turbulent region with reduced energy for downstream turbines. Strategies for increasing the efficiency of wind farms by mitigating wake effects have been the subject of much computational research. To this end, both the positioning of the turbines and their cooperative control must be taken into account. Since they are mutually dependent, increasing attention has been paid to the joint consideration of layout design and control. However, joint modeling approaches lead to large-scale and difficult optimization problems, which lack efficient solution strategies. This paper describes an efficient optimization framework for the joint design and steady-state control of wind turbines under a continuous wake effect model. Through a multi-level reformulation of the joint optimization problem, it shows how problem sub-structure can be efficiently exploited to yield order-of-magnitude reduction in convergence times over naive approaches and prior proposals.

Mixed Binary Quadratic Programs (MBQPs) are a class of NP-hard problems that arise in a wide range of applications, including finance, machine learning, and chemical and energy systems. Large-scale MBQPs are challenging to solve with exact algorithms due to the combinatorial search space and nonlinearity. Primal heuristics have been developed to quickly identify high-quality solutions to challenging combinatorial optimization problems. In this paper, we propose an extension for two well-established rounding-based primal heuristics, RENS and Undercover. Instead of using the optimal solution to a relaxation for variable rounding and search as in RENS, we use a suboptimal relaxation solution of the MBQP as the basis for rounding and guidance for searching over a restricted subproblem where a certain percentage of binary variables are free. We apply a similar idea to the Undercover heuristic that fixes a variable cover to the rounded relaxation values. Instead, we relax a subset of the cover variables based on the suboptimal relaxation and search over a larger restricted subproblem. We evaluate our proposed methods on synthetic MBQP benchmarks and real-world wind farm layout optimization problem instances. The results show that our proposed heuristics identify high-quality solutions within a small time limit and significantly reduce the primal gap and primal integral compared to RENS, Undercover, and solvers with additional primal heuristics integrated inside Branch-and-Bound.

We present differentiable predictive control (DPC), a method for offline learning of constrained neural control policies for nonlinear dynamical systems with performance guarantees. We show that the sensitivities of the parametric optimal control problem can be used to obtain direct policy gradients. Specifically, we employ automatic differentiation (AD) to efficiently compute the sensitivities of the model predictive control (MPC) objective function and constraints penalties. To guarantee safety upon deployment, we derive probabilistic guarantees on closed-loop stability and constraint satisfaction based on indicator functions and Hoeffding’s inequality. We empirically demonstrate that the proposed method can learn neural control policies for various parametric optimal control tasks. In particular, we show that the proposed DPC method can stabilize systems with unstable dynamics, track time-varying references, and satisfy nonlinear state and input constraints. Our DPC method has practical time savings compared to alternative approaches for fast and memory-efficient controller design. Specifically, DPC does not depend on a supervisory controller as opposed to approximate MPC based on imitation learning. We demonstrate that, without losing performance, DPC is scalable with greatly reduced demands on memory and computation compared to implicit and explicit MPC while being more sample efficient than model-free reinforcement learning (RL) algorithms.

Physics-informed machine learning (PIML) is a set of methods and tools that systematically integrate machine learning (ML) algorithms with physical constraints and abstract mathematical models developed in scientific and engineering domains. As opposed to purely data-driven methods, PIML models can be trained from additional information obtained by enforcing physical laws such as energy and mass conservation. More broadly, PIML models can include abstract properties and conditions such as stability, convexity, or invariance. The basic premise of PIML is that the integration of ML and physics can yield more effective, physically consistent, and data-efficient models. This paper aims to provide a tutorial-like overview of the recent advances in PIML for dynamical system modeling and control. Specifically, the paper covers an overview of the theory, fundamental concepts and methods, tools, and applications on topics of: 1) physics-informed learning for system identification; 2) physics-informed learning for control; 3) analysis and verification of PIML models; and 4) physics-informed digital twins. The paper is concluded with a perspective on open challenges and future research opportunities.

With recent advances in deep learning and large-scale computing, learning-based controls have become increasingly attractive for complex physical systems. Consequently, developing generalized learning-based control software that takes into account the next generation of computing architectures is paramount. Specifically, for the case of complex control, we present the Easily eXtendable Architecture for Reinforcement Learning (EXARL), which aims to support various scientific applications seeking to leverage reinforcement learning (RL) on exascale computing architectures. We demonstrate the efficacy and performance of the EXARL library for the scientific use case of designing a complex control policy to stabilize a power system after experiencing a fault. We use a parallel augmented random search method developed within EXARL and present its preliminary validation and performance stabilization of a fault for the IEEE 39-bus system.

Networked dynamical systems are common throughout science in engineering; e.g., biological networks, reaction networks, power systems, and the like. For many such systems, nonlinearity drives populations of identical (or near-identical) units to exhibit a wide range of nontrivial behaviors, such as the emergence of coherent structures (e.g., waves and patterns) or otherwise notable dynamics (e.g., synchrony and chaos). In this work, we seek to infer (i) the intrinsic physics of a base unit of a population, (ii) the underlying graphical structure shared between units, and (iii) the coupling physics of a given networked dynamical system given observations of nodal states. These tasks are formulated around the notion of the Universal Differential Equation, whereby unknown dynamical systems can be approximated with neural networks, mathematical terms known a priori (albeit with unknown parameterizations), or combinations of the two. We demonstrate the value of these inference tasks by investigating not only future state predictions but also the inference of system behavior on varied network topologies. The effectiveness and utility of these methods are shown with their application to canonical networked nonlinear coupled oscillators.

The future of high-performance computing (HPC) will be driven by the convergence of physical simulation, artificial intelligence (AI), machine learning (ML), and data science computing capabilities. While computational performance gains afforded by technology scaling, as predicted by Moore's Law, have enabled large scale HPC system design and deployment using commodity CPU and GPU processing components, emerging technologies will be required to effectively support such converged workloads. These emerging technologies will integrate commodity computing components with custom processing and networking accelerators into ever-more heterogeneous architectures resulting in a diverse ecosystem of industry technology developers, university, and U.S. Government researchers. In this article, we describe efforts at the U.S. Department of Energy's Pacific Northwest National Laboratory (PNNL) to construct an end-to-end codesign framework that lays a groundwork for such an ecosystem, including notable outcomes, remaining challenges, and future opportunities.

In this paper, we provide sufficient conditions for dissipativity and local asymptotic stability of discrete-time dynamical systems parametrized by deep neural networks. We leverage the representation of neural networks as pointwise affine maps, thus exposing their local linear operators and making them accessible to classical system analytic and design methods. This allows us to “crack open the black box” of the neural dynamical system’s behavior by evaluating their dissipativity, and estimating their stationary points and state-space partitioning. We relate the norms of these local linear operators to the energy stored in the dissipative system with supply rates represented by their aggregate bias terms. Empirically, we analyze the variance in dynamical behavior and eigenvalue spectra of these local linear operators with varying weight factorizations, activation functions, bias terms, and depths.