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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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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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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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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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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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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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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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