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Closing the gap between SGP4 and high-precision propagation via differentiable programming

ACTA ASTRONAUTICA 2025年 226卷 694-701页

作者： Acciarini, Giacomo Baydin, Atilim Gunes Izzo, Dario Univ Surrey Surrey Space Ctr Stag HillUniv Campus Guildford GU2 7XH England European Space Agcy Adv Concepts Team Keplerlaan 1 NL-2201 AZ Noordwijk Netherlands Univ Oxford Dept Comp Sci Parks Rd Oxford OX1 3PJ England

The simplified general perturbations 4 (SGP4) orbital propagation model is one of the most widely used methods for rapidly and reliably predicting the positions and velocities of objects orbiting Earth. Over time, SGP models have undergone refinement to enhance their efficiency and accuracy. Nevertheless, they still do not match the precision offered by high-precision numerical propagators, which can predict the positions and velocities of space objects in low-Earth orbit with significantly smaller errors. In this study, we introduce a novel differentiable version of SGP4, named d SGP4. By porting the source code of SGP4 into a differentiable program based on PyTorch, we unlock a whole new class of techniques enabled by differentiable orbit propagation, including spacecraft orbit determination, state conversion, covariance similarity transformation, state transition matrix computation, and covariance propagation. Besides differentiability, our d SGP4 supports parallel propagation of a batch of two-line elements (TLEs) in a single execution and it can harness modern hardware accelerators like GPUs or XLA devices (e.g. TPUs) thanks to running on the PyTorch backend. Furthermore, the design of d SGP4 makes it possible to use it as a differentiable component in larger machine learning (ML) pipelines, where the propagator can be an element of a larger neural network that is trained or fine-tuned with data. Consequently, we propose a novel orbital propagation paradigm, ML-d SGP4. In this paradigm, the orbital propagator is enhanced with neural networks attached to its input and output. Through gradient-based optimization, the parameters of this combined model can be iteratively refined to achieve precision surpassing that of SGP4. Fundamentally, the neural networks function as identity operators when the propagator adheres to its default behavior as defined by SGP4. However, owing to the differentiability ingrained within d SGP4, the model can be fine-tuned with ephemeris

关键词： SGP4 Orbital propagation differentiable programming Machine learning Spacecraft collision avoidance Kessler Kessler syndrome AI for space Applied machine learning for space

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THB-DiFF: a GPU-accelerated differentiable programming framework for THB-splines

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ENGINEERING WITH COMPUTERS 2024年第6期40卷 3477-3493页

作者： Moola, Ajith Balu, Aditya Krishnamurthy, Adarsh Pawar, Aishwarya Iowa State Univ Ames IA USA

We have developed a differentiable programming framework for truncated hierarchical B-splines (THB-splines), which can be used for several applications in geometry modeling, such as surface fitting and deformable image registration, and can be easily integrated with geometric deep learning frameworks. differentiable programming is a novel paradigm that enables an algorithm to be differentiated via automatic differentiation, i.e., using automatic differentiation to compute the derivatives of its outputs with respect to its inputs or parameters. differentiable programming has been used extensively in machine learning for obtaining gradients required in optimization algorithms such as stochastic gradient descent (SGD). While incorporating differentiable programming with traditional functions is straightforward, it is challenging when the functions are complex, such as splines. In this work, we extend the differentiable programming paradigm to THB-splines. THB-splines offer an efficient approach for complex surface fitting by utilizing a hierarchical tensor structure of B-splines, enabling local adaptive refinement. However, this approach brings challenges, such as a larger computational overhead and the non-trivial implementation of automatic differentiation and parallel evaluation algorithms. We use custom kernel functions for GPU acceleration in forward and backward evaluation that are necessary for differentiable programming of THB-splines. Our approach not only improves computational efficiency but also significantly enhances the speed of surface evaluation compared to previous methods. Our differentiable THB-splines framework facilitates faster and more accurate surface modeling with local refinement, with several applications in CAD and isogeometric analysis.

关键词： Truncated-hierarchical B-splines differentiable programming Surface fitting Adaptive refinement

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Neural-Integrated Meshfree (NIM) Method: A differentiable programming-based hybrid solver for computational mechanics

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2024年 427卷

作者： Du, Honghui He, Qizhi Univ Minnesota Dept Civil Environm & Geoengn 500 Pillsbury Dr SE Minneapolis MN 55455 USA

While deep learning and data -driven modeling approaches based on deep neural networks (DNNs) have recently attracted increasing attention for solving partial differential equations, their practical applications to real -world scientific and engineering problems remain limited due to the relatively low accuracy and high computational costs. In this study, we present a differentiable programming -based hybrid meshfree approach within the field of computational mechanics. This approach seamlessly integrates neural network -based deep learning architectures with physics -based meshfree discretization techniques, thus referred to as the neural -integrated meshfree (NIM) method. To effectively approximate the solution, NIM employs a hybrid scheme called NeuroPU approximation, which combines continuous DNN representations with partition of unity (PU) basis functions associated with the underlying spatial discretization. This neural -numerical hybridization not only enhances the solution representation through functional space decomposition but also reduces both the size of DNN model and the need of automatic differentiation for spatial gradient computations, leading to a significant improvement in training efficiency. Under the NIM framework, we propose two truly meshfree solvers: the strong form -based NIM (S-NIM) and the local variational form -based NIM (V-NIM). In the S-NIM solver, the strong -form governing equation is directly considered in the loss function, while the V-NIM solver employs a local Petrov-Galerkin approach that allows the construction of variational residuals based on arbitrary overlapping subdomains. This ensures both the satisfaction of underlying physics and the preservation of the meshfree property. We perform extensive numerical experiments on both stationary and transient benchmark problems to assess the effectiveness of the proposed NIM methods in terms of accuracy, scalability, generalizability, and convergence properties. Moreover, comparati

关键词： differentiable programming Meshfree methods Hybrid approximation Physics-informed learning Variational formulation Surrogate model

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differentiable programming and density matrix based Hartree–Fock method

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Chinese Physics B 2021年第6期30卷 249-254页

作者： Hong-Bin Ren Lei Wang Xi Dai Beijing National Laboratory for Condensed Matter Physics and Institute of Physics Chinese Academy of SciencesBeijing 100190China School of Physical Sciences University of Chinese Academy of SciencesBeijing 100049China Songshan Lake Materials Laboratory Dongguan 523808China Department of Physics Hong Kong University of Science and TechnologyClear Water BayKowloon 999077Hong KongChina

differentiable programming is an emerging programming paradigm that allows people to take derivative of an output of arbitrary code snippet with respect to its input. It is the workhorse behind several well known deep learning frameworks,and has attracted significant attention in scientific machine learning community. In this paper, we introduce and implement a density matrix based Hartree–Fock method that naturally fits into the demands of this paradigm, and demonstrate it by performing fully variational ground state calculation on several representative chemical molecules.

关键词： differentiable programming quantum chemistry

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differentiable programming for functional connectomics 2

Differentiable programming for functional connectomics

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2nd Machine Learning for Health (ML4H) Symposium

作者： Ciric, Rastko Thomas, Armin W. Esteban, Oscar Poldrack, Russell A. Stanford Univ Dept Bioengn Stanford CA 94305 USA Stanford Univ Stanford Data Sci Stanford CA USA Univ Lausanne Dept Radiol Lausanne Switzerland Stanford Univ Dept Psychol Stanford CA USA

Mapping the functional connectome has the potential to uncover key insights into brain organisation. However, existing workflows for functional connectomics are limited in their adaptability to new data, and principled workflow design is a challenging combinatorial problem. We introduce an analytic paradigm that implements common operations used in functional connectomics as fully differentiable processing blocks. Under this paradigm, workflow configurations exist as reparameterisations of a differentiable functional that interpolates them. The differentiable program that we ultimately envision occupies a niche midway between traditional pipelines and end-to-end neural networks, combining the glass-box tractability and domain knowledge of the former with the amenability to optimisation of the latter. In this preliminary work, we provide a proof of concept for differentiable connectomics, demonstrating the capacity of our processing blocks across three separate problem domains critically important to brain mapping. We also provide a software library to facilitate adoption. Our differentiable framework is competitive with state-of-the-art methods in functional brain parcellation, time series denoising, and covariance modelling. Taken together, our results demonstrate the promise of differentiable programming for functional connectomics.

关键词： fMRI brain connectivity differentiable programming self-supervised parcellation

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differentiable programming A LA MOREAU 47

DIFFERENTIABLE PROGRAMMING A LA MOREAU

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47th IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

作者： Roulet, Vincent Harchaoui, Zaid Univ Washington Dept Stat Seattle WA 98195 USA

ISBN: (纸本)9781665405409

The notion of a Moreau envelope is central to the analysis of first-order optimization algorithms for machine learning and signal processing. We define a compositional calculus adapted to Moreau envelopes and show how to apply it to deep networks, and, more broadly, to learning systems equipped with automatic differentiation and implemented in the spirit of differentiable programming.

关键词： Moreau envelope differentiable programming mathematical optimization deep learning

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LAGrad: Statically Optimized differentiable programming in MLIR 2023

LAGrad: Statically Optimized Differentiable Programming in M...

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32nd ACM SIGPLAN International Conference on Compiler Construction (CC)

作者： Peng, Mai Jacob Dubach, Christophe McGill Univ Montreal PQ Canada Mila Montreal PQ Canada

ISBN: (纸本)9798400700880

Automatic differentiation (AD) is a central algorithm in deep learning and the emerging field of differentiable programming. However, the performance of AD remains a significant bottleneck in these fields. Training large models requires repeatedly evaluating gradients via AD potentially millions of times. Additionally, the most common form of AD incurs an asymptotically large memory cost relative to the original function being differentiated. This paper introduces LAGrad, a reverse-mode, source-to-source AD system that leverages high-level information in MLIR to produce efficient differentiated code. LAGrad employs a collection of novel static optimizations that benefit from the semantics of high-level MLIR dialects to exploit the sparsity and structured control flow of generated code. Using these, LAGrad is able to achieve speedups of up to 2.8x and use 35x less memory relative to state of the art AD systems on real-world machine learning and computer vision benchmarks.

关键词： automatic differentiation MLIR differentiable programming static analysis sparsity

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Primal-Dual differentiable programming for Distribution System Critical Load Restoration

Primal-Dual Differentiable Programming for Distribution Syst...

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IEEE-Power-and-Energy-Society General Meeting (PESGM)

作者： Zhang, Xiangyu Knueven, Bernard Zamzam, Ahmed Reynolds, Matthew Jones, Wesley

ISBN: (纸本)9781665464413

Swift and reliable critical load restoration (CLR) can help make a distribution system resilient towards extreme events. To optimally achieve that, alongside practical concerns such as limiting online computational burden, some studies leverage model-free reinforcement learning (RL) to train control policies. Despite the advantages provided by RL algorithms, these approaches suffer from two issues: 1) the lack of a proper mechanism for constraint enforcement, and 2) poor sample efficiency. Therefore, in this paper, a primal-dual differentiable programming (PDDP) method is developed for guiding the training leading to a constraint-satisfying policy. Additionally, the model-based nature of the proposed method aims at improving sample efficiency. The experiment on a CLR problem demonstrates that PDDP can effectively train a control policy that both achieves desirable performance and satisfies required constraints.

关键词： grid resilience load restoration differentiable programming primal-dual method reinforcement learning

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Novel machine learning and differentiable programming techniques applied to the VIP-2 underground experiment

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MEASUREMENT SCIENCE AND TECHNOLOGY 2024年第2期35卷 025501-025501页

作者： Napolitano, Fabrizio Bazzi, Massimiliano Bragadireanu, Mario Cargnelli, Michael Clozza, Alberto De Paolis, Luca Del Grande, Raffaele Fiorini, Carlo Guaraldo, Carlo Iliescu, Mihail Laubenstein, Matthias Manti, Simone Marton, Johann Miliucci, Marco Piscicchia, Kristian Porcelli, Alessio Scordo, Alessandro Sgaramella, Francesco Sirghi, Diana Laura Sirghi, Florin Doce, Oton Vazquez Zmeskal, Johann Curceanu, Catalina INFN Lab Nazl Frascati Via E Fermi 54 I-00044 Frascati Rome Italy IFIN HH Inst Natl Pentru Fiz Inginerie Nucl Horia Hulubei Str Atomistilor 407 Bucharest Romania Stefan Meyer Inst Subatom Phys Austrian Acad Sci Kegelgasse 27 A-1030 Vienna Austria Tech Univ Munich Phys Dept E62 James Franck Str 1 D-85748 Garching Germany Dipartimento Elettron Informaz & Bioingn Politecn Milano I-20133 Milan Italy INFN Sez Milano I-20133 Milan Italy INFN Lab Nazl Gran Sasso Via G Acitelli 22 I-67100 Assergi Laquila Italy Ctr Ric Enr Fermi Museo Stor Fis Ctr Studi & Ric Enr Fermi Via Panisperna 89a I-00184 Rome Roma Italy Italian Space Agcy Via PolitecnS n c I-00133 Rome Roma Italy

In this work, we present novel machine learning and differentiable programming enhanced calibration techniques used to improve the energy resolution of the Silicon Drift Detectors (SDDs) of the VIP-2 underground experiment at the Gran Sasso National Laboratory. We achieve for the first time a full width at half maximum in VIP-2 below 180 eV at 8 keV, improving around 10 eV on the previous state-of-the-art. SDDs energy resolution is a key parameter in the VIP-2 experiment, which is dedicated to searches for physics beyond the standard quantum theory, targeting Pauli exclusion principle violating atomic transitions. Additionally, we show that this method can correct for potential miscalibrations, requiring less fine-tuning with respect to standard methods.

关键词： VIP-2 SDD silicon drift detector differentiable programming

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Learning closure relations using differentiable programming: An example in radiation transport

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JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER 2024年 318卷

作者： Crilly, A. J. Duhig, B. Bouziani, N. Imperial Coll Ctr Inertial Fus Studies Blackett Lab London SW7 2AZ England Imperial Coll London I X Ctr AI Sci White City Campus84 Wood Lane London W12 0BZ England Imperial Coll Dept Math London SW7 2AZ England

Reduced order models with a-priori unknown closure relations are ubiquitous in transport problems. In this work, we present a machine-learning approach to finding closure relations utilising differentiable programming. We use the Su Olson radiation transport test problem as an example training data set. We present novel closures for second angular moment (variable Eddington factor), third angular moment and flux-limited diffusion models. We evaluate the improvement of the machine-learnt closures over those from the literature. These improvements are then tested by considering a modification to the Su Olson problem. Comparisons to literature closures show the machine learning models out-perform them in both the trained and unseen problems.

关键词： Radiative transfer Machine Learning differentiable programming Reduced order models Closure relations Flux limiters

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