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DOE OSTI2020

Solving gyrokinetic systems with higher-order time dependence

We discuss theoretical and numerical aspects of gyrokinetics as a Lagrangian field theory when the field perturbation is introduced into the symplectic part. A consequence is that the field equations and particle equations of motion in general depend on the time derivatives of the field. The most well-known example is when the parallel vector potential is introduced as a perturbation, where a time derivative of the field arises only in the equations of motion, so an explicit equation for the fields may still be written. We will consider the conceptually more problematic case where the time-dependent fields appear in both the field equations and equations of motion, but where the additional term in the field equations is formally small. The conceptual issues were described by Burby (J. Plasma Phys., vol. 82 (3), 2016, 905820304): these terms lead to apparent additional degrees of freedom to the problem, so that the electric field now requires an initial condition, which is not required in low-frequency (Darwin) Vlasov–Maxwell equations. Also, the small terms in the Euler–Lagrange equations are a singular perturbation, and these two issues are interlinked. For well-behaved problems the apparent additional degrees of freedom are spurious, and the physically relevant solution may be directly identified. Because we needed to assume that the system is well behaved for small perturbations when deriving gyrokinetic theory, we must continue to assume that when solving it, and the physical solutions are thus the regular ones. The spurious nature of the singular degrees of freedom may also be seen by changing coordinate systems so the varying field appears only in the Hamiltonian. We then describe how methods appropriate for singular perturbation theory may be used to solve these asymptotic equations numerically. We then describe a proof-of-principle implementation of these methods for an electrostatic strong-flow gyrokinetic system; two basic test cases are presented to illustrate code functionality.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Quantum field theory with the generalized uncertainty principle II: Quantum Electrodynamics

Highlights: • Relativistic Generalized Uncertainty Principle gives Frame independent minimum length. • Quantum Gravity modified Dirac equation from Modified Klein–Gordon Equations. • There exists a Quantum Gravity modified Lagrangian for a spinor field theory. • Feynman vertices contain 2 fermions & up to 5 gauge bosons are allowed. • Minimum length modifies the amplitude of Electrodynamic electron–muon scattering. Continuing our earlier work on the application of the Relativistic Generalized Uncertainty Principle (RGUP) to quantum field theories, in this paper we study Quantum Electrodynamics (QED) with minimum length. We obtain expressions for the Lagrangian, Feynman rules and scattering amplitudes of the theory, and discuss their consequences for current and future high energy physics experiments. We hope this will provide an improved window for testing Quantum Gravity effects in the laboratory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Discovering causal structure with reproducing-kernel Hilbert space ε -machines

We merge computational mechanics’ definition of causal states (predictively equivalent histories) with reproducing-kernel Hilbert space (RKHS) representation inference. The result is a widely applicable method that infers causal structure directly from observations of a system’s behaviors whether they are over discrete or continuous events or time. A structural representation—a finite- or infinite-state kernel ϵ-machine—is extracted by a reduced-dimension transform that gives an efficient representation of causal states and their topology. In this way, the system dynamics are represented by a stochastic (ordinary or partial) differential equation that acts on causal states. We introduce an algorithm to estimate the associated evolution operator. Paralleling the Fokker–Planck equation, it efficiently evolves causal-state distributions and makes predictions in the original data space via an RKHS functional mapping. We demonstrate these techniques, together with their predictive abilities, on discrete-time, discrete-value infinite Markov-order processes generated by finite-state hidden Markov models with (i) finite or (ii) uncountably infinite causal states and (iii) continuous-time, continuous-value processes generated by thermally driven chaotic flows. The method robustly estimates causal structure in the presence of varying external and measurement noise levels and for very high-dimensional data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Catalyst and reactor design considerations for selective production of acids by oxidative cleavage of alkenes and unsaturated fatty acids with H 2 O 2

Oxidative cleavage of alkenes and unsaturated fatty acids with hydrogen peroxide gives an efficient and sustainable process to obtain mono- and di-acids for polymers and lubricants with fewer safety risks and less environmental impact than processes that utilize ozone or other inorganic oxidizers (e.g., permanganate, dichromate, etc.). Guided by insight into the mechanisms for competing reaction pathways (i.e., epoxidation of alkene on W–(η 2 -O 2 ) complexes vs. H 2 O 2 decomposition) and the apparent kinetics derived from kinetic experiments, here, we postulate that W-based heterogeneous catalysts can provide high performance and stable operations at low H 2 O 2 concentrations. Semi-batch reactors with continuous introduction of H 2 O 2 solutions offer the means to maintain low H 2 O 2 concentrations while providing sufficient quantities of H 2 O 2 to satisfy the reaction stoichiometry. We derived simple kinetic model equations for the epoxidation, ring-opening, oxidative cleavage, and oxidation steps and fit theses equations to batch experimental data to obtain kinetic parameters. Furthermore, this kinetic model describes the concentration profiles of reactant, oxidant, and products well as shown by agreement with experimental data. Further predictions of the optimal H 2 O 2 feed rate for semi-batch operation utilized by the proposed rate expressions and the reactor design equations suggest that low H 2 O 2 feed rate increases selectivity towards oxidative cleavage products and selective use of H 2 O 2 for oxidative cleavage pathway. Comparisons of oxidative cleavage of 4-octene in batch and semi-batch reactors show that semibatch reactors with optimized molar feed rates of H 2 O 2 increased oxidative cleavage product selectivities (76% to 99%; with an increase in butyric acid selectivity from 1% to 55%) and H 2 O 2 selectivity (3% to 30%). In addition, semibatch reaction conditions used avoid H 2 O 2 -mediated dissolution of W-atoms from the catalyst. Analysis of these findings suggest that solid oxide catalysts will be effective for continuous oxidative cleavage reactions if deployed within fixed-bed reactors that allow for distributed introduction of reactants and therefore low in situ concentrations of H 2 O 2 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

A finite scale model for shock structure

In this paper we explore the use of a finite scale model of fluid dynamics to predict the finite structure of a shock wave in a perfect gas. We begin by documenting the history and issues that have arisen when Navier–Stokes theory is applied to the shock structure problem, and continue by motivating the improvement that finite scale theory might provide from its representation of inviscid (anomalous) dissipation. Furthermore, our primary results include the formulation of a traveling wave equation from finite scale theory, an analysis of the solutions of that equation as regards shock width and monotonicity properties, and an estimation of the critical parameter of the theory from experimental data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Alternating Direction Decomposition with Strong Bounding and Convexification (ADDSBC) for Solving Security Constrained AC Unit Commitment Problems

This project aims to develop efficient and robust computational methods for solving the security-constrained unit commitment and alternating current optimal power flow problem (SC-UC-ACOPF). The SC-UC-ACOPF problem is at the center of the short-term operation of the U.S. Power Grid. It is solved every week, every day, and every 10 minutes to plan for the optimal action of electricity generation and consumption by minimizing the generation cost and maintaining power system reliability against potential disruptions of equipment failures. In mathematical terms, SC-UC-ACOPF is a challenging large-scale mixed-integer nonlinear optimization model. This means that the decisions involve both discrete variables, e.g. the turning on and off of generators and switching of transmission lines and transformers, and continuous decisions, e.g. the amount of energy generated by each generator and the power flows in the power grid. The physics of the power flow is described by nonlinear equations involving real and reactive power and bus voltages. Another key feature is the large number of contingencies, i.e. the system needs to stay reliable in face of failure of any one equipment, such as transmission lines and generators. The U.S. power grids are extremely complicated and large scale with more than 5,000 generators, 50,000 buses, and 100,000 high-voltage transmission lines, making the SC-UC-ACOPF a very large-scale computation challenge. The research developed in this project aims to solve the SC-UC-ACOPF problems in the three timescales, i.e. weekly, daily, and every 10-min. The proposed computational methods are built on a principled algorithmic approach of decomposition and penalization. More specifically, the algorithm develops spatial and temporal decomposition by exploiting the strong temporal coupling and weak spatial coupling of the UC problem and the complementary feature, i.e. weak temporal coupling and strong spatial coupling of the ACOPF problem. The algorithm also leverages recent progresses in strong convex relaxation of ACOPF. A unique feature of the proposed approach is that it generates a valid, global upper bound on the optimal maximum profit. In this way, a global optimality gap is available to measure the quality of the solution. To further speed up computation, the research team has developed a plethora of effective heuristics to strengthen the iterative penalty-based decomposition framework. For instance, a heuristic is developed to construct inner approximations of the time coupling constraints within the time decoupled problems. Contingencies are pre-screened and low-rank matrix computation is exploited to find the almost unique solution to each contingency. A novel heuristic for line switching is proposed and tested with positive impacts on instances where line switching is beneficial. Taking a systematic approach and carefully handling every detail of the problem pays off. The TIM-GO’s performance throughout the trials and the final event was stellar. TIM-GO garnered the second highest total prize money and is ranked in the top three positions across all categories of comparison.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Computational Algorithms for Unit Commitment with AC Power Flows (Final Report)

Security-constrained unit commitment (SCUC) is a key component in power system operations. When AC power flow constraints are considered in the SCUC model (AC-SCUC), the problem becomes extremely difficult due to its discrete and non-convex nature, as described in “Grid Optimization Competition Challenge 3 Problem Formulation (GOCC)”. There are four main challenges: (i) Discrete decisions regarding unit online/offline status and start-up/shut-down procedures for every single unit. The number of discrete decision variables increases considerably when a system integrates multiple generators; (ii) Configuration-based combined-cycle formulations, and multi-commodity models that include ramping products, spin/non-spin products, and regulation up/down products. The combined-cycle units introduce additional discrete decision variables and auxiliary service products further complicate the model by connecting multi-commodity products’ continuous and discrete variables; (iii) SCUC models with AC power flow constraints are far more complex due to massive bilinear terms in the large-scale nonlinear power balance equations. The nonlinear power balance equations are further complicated by the discrete step control variables of shunts; (iv) N − 1 contingency analysis. The size of the model increases linearly with the number of contingencies considered, greatly increasing the size of the optimization model. Accordingly, there is an emergent need to develop a robust algorithm capable of deriving a high-quality solution in a short time and passing through contingency tests simultaneously. In this project, we explore innovative techniques to address this challenging problem by integrating advanced polyhedral theory, approximation methods, relaxation strategies, decomposition techniques, and parallel computing. Each technique approaches the problem from a different perspective, leveraging its specific strengths to tackle distinct challenges. Each individual method has demonstrated its effectiveness in the PI’s previous research. Their integration is expected to significantly reduce the computational time required to solve the proposed complex problem. Successful completion of this project has the potential to transform the industry by enhancing optimization solvers capable of handling large-scale day-ahead energy market clearing models within strict time constraints, while incorporating AC power flow constraints. This advancement will lead to reduced overall generation costs and, consequently, increased social welfare.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2022

Robotic Planning under Uncertainty in Spatiotemporal Environments in Expeditionary Science

In the expeditionary sciences, spatiotemporally varying environments -- hydrothermal plumes, algal blooms, lava flows, or animal migrations -- are ubiquitous. Mobile robots are uniquely well-suited to study these dynamic, mesoscale natural environments. We formalize expeditionary science as a sequential decision-making problem, modeled using the language of partially-observable Markov decision processes (POMDPs). Solving the expeditionary science POMDP under real-world constraints requires efficient probabilistic modeling and decision-making in problems with complex dynamics and observational models. Previous work in informative path planning, adaptive sampling, and experimental design have shown compelling results, largely in static environments, using data-driven models and information-based rewards. However, these methodologies do not trivially extend to expeditionary science in spatiotemporal environments: they generally do not make use of scientific knowledge such as equations of state dynamics, they focus on information gathering as opposed to scientific task execution, and they make use of decision-making approaches that scale poorly to large, continuous problems with long planning horizons and real-time operational constraints. In this work, we discuss these and other challenges related to probabilistic modeling and decision-making in expeditionary science, and present some of our preliminary work that addresses these gaps. We ground our results in a real expeditionary science deployment of an autonomous underwater vehicle (AUV) in the deep ocean for hydrothermal vent discovery and characterization. Our concluding thoughts highlight remaining work to be done, and the challenges that merit consideration by the reinforcement learning and decision-making community.

Preston, Victoria↗

DOE OSTI2026

Hector V 3.5.0: Equations & Parameters

Originally introduced by Hartin et al. [2015], Hector is a community Reduced Complexity Model (RCM) designed to simulate changes in Earth’s energy balance and carbon cycle. It is maintained and developed by the Pacific Northwest National Laboratory. Hector has continued to evolve with the advances in science, leading to different releases over the years. The latest version documented in a peer-reviewed publication is Hector V3.2.0, as described by Dorheim et al. [2024].

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Efficient Simulation of Open Quantum Systems on NISQ Trapped‐Ion Hardware

Abstract Simulating open quantum systems, which interact with external environments, presents significant challenges on noisy intermediate‐scale quantum (NISQ) devices due to limited qubit resources and noise. In this study, an efficient framework is proposed for simulating open quantum systems on NISQ hardware by leveraging a time‐perturbative Kraus operator representation of the system's dynamics. This approach avoids the computationally expensive Trotterization method and exploits the Lindblad master equation to represent time evolution in a compact form, particularly for systems satisfying specific commutation relations. The efficiency of this method is demonstrated by simulating quantum channels, such as the continuous‐time Pauli channel and damped harmonic oscillators, on NISQ trapped‐ion hardware, including IonQ Harmony and Quantinuum H1‐1. Additionally, hardware‐agnostic error mitigation techniques are introduced, including Pauli channel fitting and quantum depolarizing channel inversion, to enhance the fidelity of quantum simulations. These results show strong agreement between the simulations on real quantum hardware and exact solutions, highlighting the potential of Kraus‐based methods for scalable and accurate simulation of open quantum systems on NISQ devices. This framework opens pathways for simulating more complex systems under realistic conditions in the near term.

Burdine, Colin [Department of Electrical and Compu↗

DOE OSTI2025

Harvesting Subsea Water Motion to Provide Clean Electrical Power

This TEAMER project had three main objectives related to characterizing the performance of a vortex-induced vibration (VIV) marine energy harvesting device called the Whatever Input To Torsion (WITT). The first was to characterize the motion of the WITT device as it vibrates on top of a pipe in a natural tidal flow. The second was to measure how much electricity the WITT device generates when it is deployed on top of a pipe that is secured to the seabed with a lander. The third objective was to measure how much electricity the WITT device generates in the same configuration but with a longer pipe. This TEAMER project succeeded in satisfying the first objective by measuring the motion of the WITT device with an inertial measurement unit (IMU) mounted in the WITT housing. The motion was described by examining changes in the acceleration, pitch, roll, and yaw, and displacement. The frequency of the motion was characterized using spectral analysis. The TEAMER project succeeded in reaching the second objective by measuring the power produced by the WITT. It is reported here as the average and maximum power in hourly intervals. WITT Energy decided to not have us pursue the third objective of testing a longer pipe because the first test was unexpectedly successful at having the system vibrate at the target frequency. A longer pipe would have resulted in a decreased frequency and therefore not have been a useful test. Based on these findings, the decision was made to keep the same pipe length for both tests and improve on other aspects of the test structure that had failed during the first test. The key finding of this TEAMER project is that the WITT is capable of generating electricity in moderate flow speeds when it is in a housing that is attached to a 2.5 m pipe and secured to the seabed by a lander. This report contains the first power values for a VIV instrument that generates electricity from a pendulum swinging at the top of a long pipe. The experiment demonstrated that the vibration frequency of the device varied with the tidal current speed, which changed throughout a given tidal cycle. This meant that the desired peak frequency was not sustained for more than one hour. The success of this TEAMER test provides evidence that continued research in the area of electricity generation from VIV holds promise as a source of marine energy for offshore applications. Future tests should focus on refining the pipe length equations and improving the power take off system of the WITT power electronics. In addition, experiments aimed at expanded testing and evaluation (e.g. longer than one month) are needed to measure the power production at higher tidal current speeds and test the system's durability.

Branch, Ruth A. (ORCID:0000000202356719)↗

DOE OSTI2023

Scattering in black hole backgrounds and higher-spin amplitudes. Part II

We continue to investigate correspondences between, on the one hand, scattering amplitudes for massive higher-spin particles and gravitons in appropriate quantum-to-classical limits, and on the other hand, classical gravitational interactions of spinning black holes according to general relativity. We first construct an ansatz for a gravitational Compton amplitude, at tree level, constrained only by locality, crossing symmetry, unitarity and consistency with the linearized-Kerr 3-point amplitude, to all orders in the black hole’s spin. We then explore the extent to which a unique classical Compton amplitude can be identified by comparing with the results of the classical process of scattering long-wavelength gravitational waves off an exact Kerr black hole, determined by appropriate solutions of the Teukolsky equation. Up to fourth order in spin, we find complete agreement with a previously conjectured exponential form of the tree-level Compton amplitude. At higher orders, we extract tree-level contributions from the Teukolsky amplitude by an analytic continuation from a physical (a/GM < 1) to a particle-like (a/GM > 1) regime. Up to the sixth order in spin, we identify a unique conservative part of the amplitude which is insensitive both to the choice of boundary conditions at the black hole horizon and to branch choices in the analytic continuation. The remainder of the amplitude is determined modulo an overall sign from a branch choice, with the sign flipping under exchanging purely ingoing and purely outgoing boundary conditions at the horizon. Along the way, we make contact with novel applications of massive spinor-helicity variables pertaining to their relation to EFT operators and (spinning) partial amplitudes.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Signature of hadron-quark crossover in binary-neutron-star mergers

Here, we study observational signatures of the hadron-quark crossover in binary-neutron-star mergers by numerical-relativity simulations with various mass configurations. We employ two equations of state (EoSs) for matter consistent with inference from the observational data. In the crossover scenario the EoS is softened in a density realized in binary-neutron-star mergers and is smoothly continued to quark matter. In the phase transition scenario without crossover, the EoS remains stiff and a first-order phase transition takes place in a density out of reach of mergers. A GW170817-like system forms a remnant massive neutron star in both scenarios, and it collapses into a black hole only in the crossover scenario due to the softening while gravitational-wave emission is strong. This difference is clearly reflected in the sudden shutdown of gravitational waves. For a given EoS, the lifetime of the merger remnant is determined primarily by the total mass of the system. Identifying these features in a variety of future events with the next generation of ground-based gravitational-wave detectors will enable us to clarify details of hadron-quark transition. The mass of the accretion disk surrounding the remnant black hole is affected not only by the lifetime of the remnant but also by the mass ratio of the system. Electromagnetic emission associated with the disk outflow will also be useful for detailed investigation of the hadron-quark transition.

QCD phase transitions↗

DOE OSTI2024

Differentiable Multiphysics Codes: A Breakthrough Technology for Simulation and Computing

This document summarizes the findings of a strategic planning exercise commissioned by the Weapons Simulation and Computing, Computational Physics (WSC/CP) program at the Lawrence Livermore National Laboratory (LLNL) in FY24. During the year, the committee met with multiple stakeholder communities to gather input, opinions, suggestions and concerns which have been incorporated throughout this document. The key findings from this exercise are summarized: • The development of multiphysics modelling and simulation (mod/sim) codes and software technologies, their deployment on exascale compute platforms, and their broad adoption across the NNSA is a major success of the Advanced Simulation and Computing (ASC) program and the Exascale Computing Project (ECP). Sustained investment in these core technologies is essential. • Today’s state of the art involves running ensembles of O(100K) simulations to perform uncertainty quantification (UQ) and design studies using multiple statistical methods such as Bayesian optimization to understand sensitivities of our models and explore parameterized design spaces. Even with exascale computing, we are practically limited to O(10) parameters in these studies since the number of simulations required to sample the space scales exponentially with the number of design parameters. • The data from these simulation ensembles is increasingly being used to train machine learned (ML) surrogates (or reduced order models, ROMs) which can then be used for optimization or real time design exploration. However, the trained surrogates are still limited in the number of parameters they can represent due to the sampling limitations previously noted. • Augmenting our suite of integrated multiphysics simulation codes, both current and emerging, with the ability to compute gradients (solution derivatives) of arbitrary simulation outputs with respect to (some or all) simulation inputs would be a breakthrough technology, opening the door to a new era of efficient and automated inverse design based on verified and validated mod/sim capabilities. • This capability, which we refer to as differentiable multiphysics codes (DMCs), would revolutionize both UQ and optimization studies by breaking the curse of dimensionality that presently limits our “gradient-free” ensemble based computing approach. A similar breakthrough occurred in the AI/ML community once the ability to compute gradients of arbitrary loss functions using back-propagation became commonplace. Gradient information from the multiphysics codes can also be used to dramatically improve the efficiency and scale of training of ML/ROM surrogates for rapid assessments. • Achieving this in our suite of codes will be a grand challenge, similar to the amount of effort that was required to transition from CPU to GPU computing. It will require buy-in from the entire WSC/CP program and beyond, including all integrated codes, physics and engineering models, third-party library dependencies and performance portability abstractions. It will also require investment in research and development of numerical methods for computing adjoints of coupled physics across multiple adaptively refined moving meshes and of stochastic (Monte Carlo) and mesh free (SPH) methods. • New software and numerical techniques, largely pioneered by the AI/ML community, make this feasible. Chief among these is automatic differentiation (AD), the ability to employ AD at point-wise locations in a physics calculation (instead of traditional black-box approaches) and the ability to perform “back-propagation in time” (or reverse mode AD) for non-linear partial differential equations (PDEs). Fundamentally, the conclusion of this strategic planning exercise is that the time is right to undertake a large scale effort in WSC, centered on the existing integrated codes, to continue the natural evolution of mod/sim in the age of AI/ML. Instead of attempting to replace mod/sim with purely data driven AI/ML models, we believe the key to success is to integrate AI/ML by building on top of the decades of hard-won knowledge and the verified/validated multiphysics modelling capability that is the hallmark of the ASC program.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Development and assessment of hierarchical multi-reward reinforcement learning based potential for silicene with state-of-the-art models

We develop a new interatomic force field for Silicene, a 2D material with a buckled hexagonal lattice structure with high polymorphism. We introduce new parameterizations of a Tersoff model using a hierarchical multi-reward reinforcement learning (RL) methodology coupled with a continuous Monte Carlo Tree Search optimization. Our model significantly outperforms existing methods by enhancing the accuracy of predictions for the structural and thermodynamic properties of seven silicene polymorphs-including structure, energy, equation of state, elasticity, and phonon dispersion-when compared to established models. We further make a comprehensive comparison of the various models in predicting the mechanical and thermal properties of silicene. We trace the origin of the improved performance to the description of the angular dependence in the bond-order term, suggesting that modifying the angular terms in short-range models is essential to capture the structural diversity in low dimensional systems.

2D materials↗

DOE OSTI2026

Energy-conserving contact dynamics of nonspherical rigid-body particles

Understanding the contact dynamics of nonspherical particles is crucial for accurately modeling colloidal and granular systems where shape anisotropy dictates structural organization and transport properties. We here introduce an energy-conserving contact dynamics framework for arbitrary convex rigid-body particles by implementing vertex–boundary interactions in 2D and vertex–surface and edge–edge detection in 3D. The established formulation enables continuous force evaluation and prevents particle overlap while conserving total energy during translational and rotational motion. We demonstrate the framework’s stability and its utility to capture packing behavior, anisotropic diffusion, and equations of state of polygonal and polyhedral particles as examples. The framework establishes a robust and extensible foundation for investigating nonequilibrium dynamics of complex nonspherical particulate systems, enabling enhanced understanding of phenomena across spatiotemporal scales in self- and directed-assembly, granular flows, and hydrodynamics, potentially coupled with interactions that represent underlying physical mechanisms.

Discrete element method↗

DOE OSTI2020

Far From Equilibrium Hydrodynamics and the Beam Energy Scan

The existence of hydrodynamic attractors in rapidly expanding relativistic systems has shed light on the success of relativistic hydrodynamics in describing heavy-ion collisions at zero chemical potential. As the search for the QCD critical point continues, it is important to investigate how out of equilibrium effects influence the trajectories on the QCD phase diagram. In this proceedings, we study a Bjorken expanding hydrodynamic system based on DMNR equations of motion with initial out of equilibrium effects and finite chemical potential in a system with a critical point. We find that the initial conditions are not unique for a specific freeze-out point, but rather the system can evolve to the same final state freeze-out point with a wide range of initial baryon chemical potential, µ B . For the same initial energy density and baryon density, depending on how far out of equilibrium the system begins, the initial µ B can vary by Δµ B ~ 350 MeV. Furthermore, our results indicate that knowledge of the out-of-equilibrium effects in the initial state provide vital information that influences the search for the QCD critical point.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Convex Q-Learning in Continuous Time with Application to Dispatch of Distributed Energy Resources

Convex Q-learning is a recent approach to reinforcement learning, motivated by the possibility of a firmer theory for convergence, and the possibility of making use of greater a priori knowledge regarding policy or value function structure. This paper explores algorithm design in the continuous time domain, with a finite-horizon optimal control objective. The main contributions are (i) The new Q-ODE: a model-free characterization of the Hamilton-Jacobi-Bellman equation. (ii) A formulation of Convex Q-learning that avoids approximations appearing in prior work. The Bellman error used in the algorithm is defined by filtered measurements, which is necessary in the presence of measurement noise. (iii) Convex Q-learning with linear function approximation is a convex program. It is shown that the constraint region is bounded, subject to an exploration condition on the training input. (iv) The theory is illustrated in application to resource allocation for distributed energy resources, for which the theory is ideally suited.

Lu, Fan↗