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A differentiable programming framework for spin models

COMPUTER PHYSICS COMMUNICATIONS 2024年 302卷

作者： Farias, Tiago S. Schultz, Vitor V. Mombach, Jose C. M. Maziero, Jonas Univ Fed Sao Carlos Ctr Exact Sci & Technol Phys Dept Rod Washington Luis km 235 BR-13565905 Sao Carlos SP Brazil Univ Fed Santa Maria Ctr Nat & Exact Sci Phys Dept Roraima Ave 1000 BR-97105900 Santa Maria RS Brazil Inst & Ctr Dev & Res Software Technol ICTS Governor Danilo Matos Areosa Ave 1199 BR-69075904 Manaus AM Brazil

We introduce a novel framework for simulating spin models using differentiable programming, an approach that leverages the advancements in machine learning and computational efficiency. We focus on three distinct spin systems: the Ising model, the Potts model, and the Cellular Potts model, demonstrating the practicality and scalability of our framework in modeling these complex systems. Additionally, this framework allows for the optimization of spin models, which can adjust the parameters of a system by a defined objective function. In order to simulate these models, we adapt the Metropolis-Hastings algorithm to a differentiable programming paradigm, employing batched tensors for simulating spin lattices. This adaptation not only facilitates the integration with existing deep learning tools but also significantly enhances computational speed through parallel processing capabilities, as it can be implemented on different hardware architectures, including GPUs and TPUs.

关键词： differentiable programming Monte Carlo simulation Ising model Cellular Potts model

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Coarsening Optimization for differentiable programming

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PROCEEDINGS OF THE ACM ON programming LANGUAGES-PACMPL 2021年第OOPSLA期5卷 1–27页

作者： Shen, Xipeng Zhang, Guoqiang Dea, Irene Andow, Samantha Arroyo-Fang, Emilio Gafter, Neal George, Johann Grueter, Melissa Meijer, Erik Shivers, Olin Grigsby Stumpos, Steffi Tempest, Alanna Warden, Christy Yang, Shannon Facebook Inc Menlo Pk CA 94025 USA North Carolina State Univ Raleigh NC 27695 USA

This paper presents a novel optimization for differentiable programming named coarsening optimization. It offers a systematic way to synergize symbolic differentiation and algorithmic differentiation (AD). Through it, the granularity of the computations differentiated by each step in AD can become much larger than a single operation, and hence lead to much reduced runtime computations and data allocations in AD. To circumvent the difficulties that control flow creates to symbolic differentiation in coarsening, this work introduces.. calculus, a novel method to allow symbolic reasoning and differentiation of computations that involve branches and loops. It further avoids "expression swell" in symbolic differentiation and balance reuse and coarsening through the design of reuse-centric segment of interest identification. Experiments on a collection of real-world applications show that coarsening optimization is effective in speeding up AD, producing several times to two orders of magnitude speedups.

关键词： differentiable programming compiler program optimizations SSA Calculus

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differentiable Quantum programming with Unbounded Loops

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ACM TRANSACTIONS ON SOFTWARE ENGINEERING AND METHODOLOGY 2024年第1期33卷 1-63页

作者： Fang, Wang Ying, Mingsheng Wu, Xiaodi Chinese Acad Sci Inst Software State Key Lab Comp Sci 4th Zhongguancun South Fourth St Beijing 100190 Peoples R China Univ Chinese Acad Sci Beijing Peoples R China Tsinghua Univ Dept Comp Sci & Technol Beijing Peoples R China Univ Maryland Dept Comp Sci College Pk MD 20740 USA Univ Maryland Joint Ctr Quantum Informat & Comp Sci College Pk MD 20740 USA

The emergence of variational quantum applications has led to the development of automatic differentiation techniques in quantum computing. Existing work has formulated differentiable quantum programming with bounded loops, providing a framework for scalable gradient calculation by quantum means for training quantum variational applications. However, promising parameterized quantum applications, e.g., quantum walk and unitary implementation, cannot be trained in the existing framework due to the natural involvement of unbounded loops. To fill in the gap, we provide the first differentiable quantum programming framework with unbounded loops, including a newly designed differentiation rule, code transformation, and their correctness proof. Technically, we introduce a randomized estimator for derivatives to deal with the infinite sum in the differentiation of unbounded loops, whose applicability in classical and probabilistic programming is also discussed. We implement our framework with Python and Q# and demonstrate a reasonable sample efficiency. Through extensive case studies, we showcase an exciting application of our framework in automatically identifying close-to-optimal parameters for several parameterized quantum applications.

关键词： Quantum programming languages differentiable programming quantum machine learning unbounded loops

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differentiable programming for online training of a neural artificial viscosity function within a staggered grid Lagrangian hydrodynamics scheme

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MACHINE LEARNING-SCIENCE AND TECHNOLOGY 2021年第2期2卷

作者： Melland, Pake Albright, Jason Urban, Nathan M. Univ Iowa Appl Math & Computat Sci Iowa City IA 52242 USA Los Alamos Natl Lab Appl Phys Los Alamos NM 87544 USA Brookhaven Natl Lab Appl Math Upton NY 11973 USA Los Alamos Natl Lab Computat Phys & Methods Los Alamos NM 87544 USA

Lagrangian methods to solve the inviscid Euler equations produce numerical oscillations near shock waves. A common approach to reducing these oscillations is to add artificial viscosity (AV) to the discrete equations. The AV term acts as a dissipative mechanism that attenuates oscillations by smearing the shock across a finite number of computational cells. However, AV introduces several control parameters that are not determined by the underlying physical model, and hence, in practice are tuned to the characteristics of a given problem. We seek to improve the standard quadratic-linear AV form by replacing it with a learned neural function that reduces oscillations relative to exact solutions of the Euler equations, resulting in a hybrid numerical-neural hydrodynamic solver. Because AV is an artificial construct that exists solely to improve the numerical properties of a hydrodynamic code, there is no offline 'viscosity data' against which a neural network can be trained before inserting into a numerical simulation, thus requiring online training. We achieve this via differentiable programming, i.e. end-to-end backpropagation or adjoint solution through both the neural and differential equation code, using automatic differentiation of the hybrid code in the Julia programming language to calculate the necessary loss function gradients. A novel offline pre-training step accelerates training by initializing the neural network to the default numerical AV scheme, which can be learned rapidly by space-filling sampling over the AV input space. We find that online training over early time steps of simulation is sufficient to learn a neural AV function that reduces numerical oscillations in long-term hydrodynamic shock simulations. These results offer an early proof-of-principle that online differentiable training of hybrid numerical schemes with novel neural network components can improve certain performance aspects existing in purely numerical schemes.

关键词： differentiable programming Lagrangian hydrodynamics hybrid modeling shock waves

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A differentiable programming method for quantum control

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MACHINE LEARNING-SCIENCE AND TECHNOLOGY 2020年第3期1卷

作者： Schafer, Frank Kloc, Michal Bruder, Christoph Lorch, Niels Univ Basel Dept Phys Klingelbergstr 82 CH-4056 Basel Switzerland

Optimal control is highly desirable in many current quantum systems, especially to realize tasks in quantum information processing. We introduce a method based on differentiable programming to leverage explicit knowledge of the differential equations governing the dynamics of the system. In particular, a control agent is represented as a neural network that maps the state of the system at a given time to a control pulse. The parameters of this agent are optimized via gradient information obtained by direct differentiation through both the neural network and the differential equation of the system. This fully differentiable reinforcement learning approach ultimately yields time-dependent control parameters optimizing a desired figure of merit. We demonstrate the method's viability and robustness to noise in eigenstate preparation tasks for three systems: a single qubit, a chain of qubits, and a quantum parametric oscillator.

关键词： scientific machine learning differentiable programming quantum control quantum parametric oscillator GHZ states

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A Simple differentiable programming Language

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PROCEEDINGS OF THE ACM ON programming LANGUAGES-PACMPL 2020年第POPL期4卷 1–28页

作者： Abadi, Martin Plotkin, Gordon D. Google Res Mountain View CA 94043 USA

Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the mathematical notion of derivative is not always entirely clear discrepancies can arise, sometimes inadvertently. In order to study automatic differentiation in such programming contexts, we define a small but expressive programming language that includes a construct for reverse-mode differentiation. We give operational and denotational semantics for this language. The operational semantics employs popular implementation techniques, while the denotational semantics employs notions of differentiation familiar from real analysis. We establish that these semantics coincide.

关键词： automatic differentiation differentiable programming

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Control of stochastic quantum dynamics by differentiable programming

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MACHINE LEARNING-SCIENCE AND TECHNOLOGY 2021年第3期2卷

作者： Schafer, Frank Sekatski, Pavel Koppenhofer, Martin Bruder, Christoph Kloc, Michal Univ Basel Dept Phys Klingelbergstr 82 CH-4056 Basel Switzerland Univ Geneva Dept Appl Phys CH-1211 Geneva Switzerland Univ Chicago Pritzker Sch Mol Engn Chicago IL 60637 USA

Control of the stochastic dynamics of a quantum system is indispensable in fields such as quantum information processing and metrology. However, there is no general ready-made approach to the design of efficient control strategies. Here, we propose a framework for the automated design of control schemes based on differentiable programming. We apply this approach to the state preparation and stabilization of a qubit subjected to homodyne detection. To this end, we formulate the control task as an optimization problem where the loss function quantifies the distance from the target state, and we employ neural networks (NNs) as controllers. The system's time evolution is governed by a stochastic differential equation (SDE). To implement efficient training, we backpropagate the gradient information from the loss function through the SDE solver using adjoint sensitivity methods. As a first example, we feed the quantum state to the controller and focus on different methods of obtaining gradients. As a second example, we directly feed the homodyne detection signal to the controller. The instantaneous value of the homodyne current contains only very limited information on the actual state of the system, masked by unavoidable photon-number fluctuations. Despite the resulting poor signal-to-noise ratio, we can train our controller to prepare and stabilize the qubit to a target state with a mean fidelity of around 85%. We also compare the solutions found by the NN to a hand-crafted control strategy.

关键词： scientific machine learning quantum control stochastic Schrodinger equation homodyne detection differentiable programming

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Efficient differentiable programming in a Functional Array-Processing Language

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PROCEEDINGS OF THE ACM ON programming LANGUAGES-PACMPL 2019年第ICFP期3卷 1-30页

作者： Shaikhha, Amir Fitzgibbon, Andrew Vytiniotis, Dimitrios Jones, Simon Peyton Univ Oxford Oxford England Microsoft Res Cambridge England DeepMind London England

We present a system for the automatic differentiation (AD) of a higher-order functional array-processing language. The core functional language underlying this system simultaneously supports both source-to-source forward-mode AD and global optimisations such as loop transformations. In combination, gradient computation with forward-mode AD can be as efficient as reverse mode, and that the Jacobian matrices required for numerical algorithms such as Gauss-Newton and Levenberg-Marquardt can be efficiently computed.

关键词： Linear Algebra differentiable programming Optimising Compilers Loop Fusion Code Motion

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Demystifying differentiable programming: Shift/Reset the Penultimate Backpropagator

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PROCEEDINGS OF THE ACM ON programming LANGUAGES-PACMPL 2019年第ICFP期3卷 1-31页

作者： Wang, Fei Zheng, Daniel Decker, James Wu, Xilun Essertel, Gregory M. Rompf, Tiark Purdue Univ W Lafayette IN 47907 USA

Deep learning has seen tremendous success over the past decade in computer vision, machine translation, and gameplay. This success rests crucially on gradient-descent optimization and the ability to "learn" parameters of a neural network by backpropagating observed errors. However, neural network architectures are growing increasingly sophisticated and diverse, which motivates an emerging quest for even more general forms of differentiable programming, where arbitrary parameterized computations can be trained by gradient descent. In this paper, we take a fresh look at automatic differentiation (AD) techniques, and especially aim to demystify the reverse-mode form of AD that generalizes backpropagation in neural networks. We uncover a tight connection between reverse-mode AD and delimited continuations, which permits implementing reverse-mode AD purely via operator overloading and without managing any auxiliary data structures. We further show how this formulation of AD can be fruitfully combined with multi-stage programming (staging), leading to an efficient implementation that combines the performance benefits of deep learning frameworks based on explicit reified computation graphs (e.g., TensorFlow) with the expressiveness of pure library approaches (e.g., PyTorch).

关键词： Delimited Continuations Multi-stage Progranuning differentiable programming Automated Differentiation

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Small Signal Equivalent Modeling for Large ES-Embedded DFIG Wind Farm With

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IEEE TRANSACTIONS ON POWER SYSTEMS 2025年第3期40卷 2205-2216页

作者： Park, Seonho Van Hentenryck, Pascal Georgia Inst Technol Sch Ind & Syst Engn Atlanta GA 30332 USA

Security-Constrained Optimal Power Flow (SCOPF) plays a crucial role in power grid stability but becomes increasingly complex as systems grow. This paper introduces Primal-Dual Learning (PDL) for SCOPF (PDL-SCOPF), a self-supervised end-to-end primal-dual learning framework for producing near-optimal solutions to large-scale SCOPF problems in milliseconds. Indeed, PDL-SCOPF remedies the limitations of supervised counterparts that rely on training instances with their optimal solutions, which becomes impractical for large-scale SCOPF problems. PDL-SCOPF mimics an Augmented Lagrangian Method (ALM) for training primal and dual networks that learn the primal solutions and the Lagrangian multipliers, respectively, to the unconstrained optimizations. In addition, PDL-SCOPF incorporates a repair layer to ensure the feasibility of the power balance in the nominal case, and a binary search layer to compute, using the Automatic Primary Response (APR), the generator dispatches in the contingencies. The resulting differentiable program can then be trained end-to-end using the objective function of the SCOPF and the power balance constraints of the contingencies. Experimental results demonstrate that the PDL-SCOPF delivers accurate feasible solutions with minimal optimality gaps. The framework underlying PDL-SCOPF aims at bridging the gap between traditional optimization methods and machine learning, highlighting the potential of self-supervised end-to-end primal-dual learning for large-scale optimization tasks.

关键词： Contingency management Generators Optimization Load flow Training Machine learning Vectors Transmission line matrix methods Power system stability Maintenance engineering Primal-dual learning security-constrained optimal power flow column and constraint generation deep learning differentiable programming end-to-end learning

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