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Tensor LISTA: differentiable sparse representation learning for multi-dimensional tensor

NEUROCOMPUTING 2021年 463卷 554-565页

作者： Zhao, Qi Liu, Guangcan Liu, Qingshan Nanjing Univ Informat Sci & Technol Sch Automat B DAT Nanjing Peoples R China

The existing algorithms for sparse coding, which aim to seek sparse representation for given multi-dimensional signal, suffer from two main defects. Vector-based algorithms, e.g., LISTA, couldn't handle the signal in tensor form well. On the other hand, tensor-based algorithms are not learnable yet, leading to high computational cost. Towards this dilemma, we propose Tensor LISTA (TLISTA) bA to a multi-dimensional tensor-based model. Benefiting from tensor representation and differentiable programming, TLISTA achieves rapid inference speed and acquires more valuable representation for the data primarily organized in tensor form. Theoretical analysis about the convergence of TLISTA is then introduced, show -ing that TLISTA can attain the linear convergence rate. Extensive experiments confirm the effectiveness and efficiency of TLISTA for tensor sparse coding. (c) 2021 Elsevier B.V. All rights reserved.

关键词： Sparse coding differentiable programming Tensor representation

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Systematically Differentiating Parametric Discontinuities

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ACM TRANSACTIONS ON GRAPHICS 2021年第4期40卷 1-18页

作者： Bangaru, Sai Praveen Michel, Jesse Mu, Kevin Bernstein, Gilbert Li, Tzu-Mao Ragan-Kelley, Jonathan MIT CSAIL 77 Massachusetts Ave Cambridge MA 02139 USA Univ Calif Berkeley Berkeley CA USA

Emerging research in computer graphics, inverse problems, and machine learning requires us to differentiate and optimize parametric discontinuities. These discontinuities appear in object boundaries, occlusion, contact, and sudden change over time. In many domains, such as rendering and physics simulation, we differentiate the parameters of models that are expressed as integrals over discontinuous functions. Ignoring the discontinuities during differentiation often has a significant impact on the optimization process. Previous approaches either apply specialized hand-derived solutions, smooth out the discontinuities, or rely on incorrect automatic differentiation. We propose a systematic approach to differentiating integrals with discontinuous integrands, by developing a new differentiable programming language. We introduce integration as a language primitive and account for the Dirac delta contribution from differentiating parametric discontinuities in the integrand. We formally define the language semantics and prove the correctness and closure under the differentiation, allowing the generation of gradients and higher-order derivatives. We also build a system, Teg, implementing these semantics. Our approach is widely applicable to a variety of tasks, including image stylization, fitting shader parameters, trajectory optimization, and optimizing physical designs.

关键词： Automatic differentiation differentiable programming differentiable graphics differentiable rendering differentiable physics domain-specific language

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Learning Stochastic Parametric differentiable Predictive Control Policies 10th

Learning Stochastic Parametric Differentiable Predictive Con...

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10th IFAC Symposium on Robust Control Design (ROCOND)

作者： Drgona, Jan Mukherjee, Sayak Tuor, Aaron Halappanavar, Mahantesh Vrabie, Draguna Pacific Northwest Natl Lab Richland WA 99352 USA

The problem of synthesizing stochastic explicit model predictive control policies is known to be quickly intractable even for systems of modest complexity when using classical control-theoretic methods. To address this challenge, we present a scalable alternative called stochastic parametric differentiable predictive control (SP-DPC) for unsupervised learning of neural control policies governing stochastic linear systems subject to nonlinear chance constraints. SP-DPC is formulated as a deterministic approximation to the stochastic parametric constrained optimal control problem. This formulation allows us to directly compute the policy gradients via automatic differentiation of the problem's value function, evaluated over sampled parameters and uncertainties. In particular, the computed expectation of the SP-DPC problem's value function is backpropagated through the closed-loop system rollouts parametrized by a known nominal system dynamics model and neural control policy which allows for direct model-based policy optimization. We demonstrate the computational efficiency and scalability of the proposed policy optimization algorithm in three numerical examples, including systems with a large number of states or subject to nonlinear constraints. Copyright (C) 2022 The Authors.

关键词： Stochastic explicit model predictive control offline model-based policy optimization deep neural networks differentiable programming parametric programming

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Beyond graph neural networks with lifted relational neural networks

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MACHINE LEARNING 2021年第7期110卷 1695-1738页

作者： Sourek, Gustav Zelezny, Filip Kuzelka, Ondrej Czech Tech Univ Fac Elect Engn Dept Comp Sci Prague Czech Republic

We introduce a declarative differentiable programming framework, based on the language of Lifted Relational Neural Networks, where small parameterized logic programs are used to encode deep relational learning scenarios through the underlying symmetries. When presented with relational data, such as various forms of graphs, the logic program interpreter dynamically unfolds differentiable computation graphs to be used for the program parameter optimization by standard means. Following from the declarative, relational logic-based encoding, this results into a unified representation of a wide range of neural models in the form of compact and elegant learning programs, in contrast to the existing procedural approaches operating directly on the computational graph level. We illustrate how this idea can be used for a concise encoding of existing advanced neural architectures, with the main focus on Graph Neural Networks (GNNs). Importantly, using the framework, we also show how the contemporary GNN models can be easily extended towards higher expressiveness in various ways. In the experiments, we demonstrate correctness and computation efficiency through comparison against specialized GNN frameworks, while shedding some light on the learning performance of the existing GNN models.

关键词： Graph neural networks Lifted relational neural networks Symmetries Datalog differentiable programming Relational learning Molecule classification

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differentiable rotamer sampling with molecular force fields

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BRIEFINGS IN BIOINFORMATICS 2024年第1期25卷 bbad456-bbad456页

作者： Sha, Congzhou M. Wang, Jian Dokholyan, Nikolay, V Penn State Coll Med Dept Pharmacol Hershey PA 17033 USA 1214 Res Blvd Hummelstown PA 17036 USA Penn State Coll Med Hershey PA USA Penn State Coll Med Pharmacol Hershey PA USA

Molecular dynamics (MD) is the primary computational method by which modern structural biology explores macromolecule structure and function. Boltzmann generators have been proposed as an alternative to MD, by replacing the integration of molecular systems over time with the training of generative neural networks. This neural network approach to MD enables convergence to thermodynamic equilibrium faster than traditional MD;however, critical gaps in the theory and computational feasibility of Boltzmann generators significantly reduce their usability. Here, we develop a mathematical foundation to overcome these barriers;we demonstrate that the Boltzmann generator approach is sufficiently rapid to replace traditional MD for complex macromolecules, such as proteins in specific applications, and we provide a comprehensive toolkit for the exploration of molecular energy landscapes with neural networks.

关键词： molecular dynamics Boltzmann generator rotameric sampling differentiable programming neural network statistical mechanics

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Automatic Differentiation in PCF

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

作者： Mazza, Damiano Pagani, Michele CNRS Paris France Univ Paris IRIF UMR CNRS 8243 Paris France Univ Sorbonne Paris Nord LIPN CNRS UMR 7030 Paris France

We study the correctness of automatic differentiation (AD) in the context of a higher-order, Turing-complete language (PCF with real numbers), both in forward and reverse mode. Our main result is that, under mild hypotheses on the primitive functions included in the language, AD is almost everywhere correct, that is, it computes the derivative or gradient of the program under consideration except for a set of Lebesgue measure zero. Stated otherwise, there are inputs on which AD is incorrect, but the probability of randomly choosing one such input is zero. Our result is in fact more precise, in that the set of failure points admits a more explicit description: for example, in case the primitive functions are just constants, addition and multiplication, the set of points where AD fails is contained in a countable union of zero sets of polynomials.

关键词： differentiable programming Lambda-Calculus Linear Logic

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Toward artificial-intelligence assisted design of experiments

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NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH SECTION A-ACCELERATORS SPECTROMETERS DETECTORS AND ASSOCIATED EQUIPMENT 2023年 1047卷

作者： Dorigo, Tommaso MODE Collaboration Ist Nazl Fis Nucl Sez Padova Via Francesco Marzolo 8 I-35131 Padua Italy

Computer science tools involving differentiable programming today enable the end-to-end modeling of the very complex instruments we develop for fundamental physics. A complete model of an experiment studying fundamental interactions usually involves a surrogate or parametric approximation of data-generating processes, along with models of detector layout, pattern recognition, and inference-extraction procedures. The resulting software pipeline enables the study of the dependence of a performance metric on detector-defining parameters and its maximization by stochastic gradient descent across the very large space of design options. The software may identify new design solutions, as well as indicate optimal compromises between cost and performance.

关键词： Optimization Detector design differentiable programming

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Gradient-based geometry learning for fan-beam CT reconstruction

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PHYSICS IN MEDICINE AND BIOLOGY 2023年第20期68卷 205004-205004页

作者： Thies, Mareike Wagner, Fabian Maul, Noah Folle, Lukas Meier, Manuela Rohleder, Maximilian Schneider, Linda-Sophie Pfaff, Laura Gu, Mingxuan Utz, Jonas Denzinger, Felix Manhart, Michael Maier, Andreas FAU Erlangen Nurnberg Pattern Recognit Lab Erlangen Germany Siemens Healthcare GmbH Erlangen Germany FAU Erlangen Nurnberg Dept AIBE Erlangen Germany

Objective. Incorporating computed tomography (CT) reconstruction operators into differentiable pipelines has proven beneficial in many applications. Such approaches usually focus on the projection data and keep the acquisition geometry fixed. However, precise knowledge of the acquisition geometry is essential for high quality reconstruction results. In this paper, the differentiable formulation of fan-beam CT reconstruction is extended to the acquisition geometry. Approach. The CT fan-beam reconstruction is analytically derived with respect to the acquisition geometry. This allows to propagate gradient information from a loss function on the reconstructed image into the geometry parameters. As a proof-of-concept experiment, this idea is applied to rigid motion compensation. The cost function is parameterized by a trained neural network which regresses an image quality metric from the motion-affected reconstruction alone. Main results. The algorithm improves the structural similarity index measure (SSIM) from 0.848 for the initial motion-affected reconstruction to 0.946 after compensation. It also generalizes to real fan-beam sinograms which are rebinned from a helical trajectory where the SSIM increases from 0.639 to 0.742. Significance. Using the proposed method, we are the first to optimize an autofocus-inspired algorithm based on analytical gradients. Next to motion compensation, we see further use cases of our differentiable method for scanner calibration or hybrid techniques employing deep models.

关键词： computed tomography projective geometry differentiable programming motion compensation

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JAX-DIPS: Neural bootstrapping of finite discretization methods and application to elliptic problems with discontinuities

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JOURNAL OF COMPUTATIONAL PHYSICS 2023年 493卷

作者： Mistani, Pouria A. Pakravan, Samira Ilango, Rajesh Gibou, Frederic Univ Calif Santa Barbara Santa Barbara CA 93106 USA Nvidia Corp Santa Clara CA 95051 USA

We present a scalable strategy for development of mesh-free hybrid neuro-symbolic partial differential equation solvers based on existing mesh-based numerical discretization methods. Particularly, this strategy can be used to efficiently train neural network surrogate models of partial differential equations by (i) leveraging the accuracy and convergence properties of advanced numerical methods, solvers, and preconditioners, as well as (ii) better scalability to higher order PDEs by strictly limiting optimization to first order automatic differentiation. The presented neural bootstrapping method (hereby dubbed NBM) is based on evaluation of the finite discretization residuals of the PDE system obtained on implicit Cartesian cells centered on a set of random collocation points with respect to trainable parameters of the neural network. Importantly, the conservation laws and symmetries present in the bootstrapped finite discretization equations inform the neural network about solution regularities within local neighborhoods of training points. We apply NBM to the important class of elliptic problems with jump conditions across irregular interfaces in three spatial dimensions. We show the method is convergent such that model accuracy improves by increasing number of collocation points in the domain and preconditioning the residuals. We show NBM is competitive in terms of memory and training speed with other PINN-type frameworks. The algorithms presented here are implemented using JAX in a software package named JAX-DIPS (https://github .com /JAXDIPS /JAX-DIPS), standing for differentiable interfacial PDE solver. We open sourced JAXDIPS to facilitate research into use of differentiable algorithms for developing hybrid PDE solvers. (c) 2023 Elsevier Inc. All rights reserved.

关键词： Level-set method Free boundary problems Surrogate models Jump conditions differentiable programming Neural networks

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Physics-integrated neural differentiable (PiNDiff) model for composites manufacturing

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2023年第1期406卷

作者： Akhare, Deepak Luo, Tengfei Wang, Jian-Xun Univ Notre Dame Dept Aerosp & Mech Engn Notre Dame IN USA Univ Notre Dame Ctr Sustainable Energy ND Energy Notre Dame IN USA Univ Notre Dame Dept Chem & Biomol Engn Notre Dame IN USA Univ Notre Dame Lucy Family Inst Data & Soc Notre Dame IN USA Univ Notre Dame Dept Aerosp & Mech Engn Notre Dame IN 46556 USA

Various manufacturing technologies are being developed to improve the manufacturing of composites owing to their low weight and high performance. The mechanical properties of the composites depend on various variables and parameters of the manufacturing process, which are challenging, if not impossible, to determine and optimize experimentally. Traditional first-principle modeling approaches are not accessible due to the complex physics involved. A hybrid model that combines incomplete physics knowledge with available measurement data within a differentiable programming framework opens up new avenues to tackle the challenges. In this work, a physics-integrated neural differentiable (PiNDiff) model is developed, where the partially known physics is integrated into the recurrent network architecture to enable effective learning and generalization. The merit and potential of the proposed method have been demonstrated in modeling the curing process of thick thermoset composite laminates, whose governing physics is partially given. The proposed PiNDiff model shows the capability to learn unknown physics from the limited, indirect data and, meanwhile, can be used to infer unobserved variables and parameters. The performance of the PiNDiff model has been compared with two state-of-the-art (SOTA) black-box deep learning models, and its advantages over the purely data-driven models and first-principles physics-based models have been discussed in detail. The demonstrated PiNDiff strategy may provide a general strategy to model phenomena where physics is only partially known and sparse, indirect data are available. (c) 2023 Elsevier B.V. All rights reserved.

关键词： Composite cure differentiable programming Neural networks Scientific machine learning Surrogate modeling Operator learning

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