Physical Gradients for Deep Learning

Holl, Philipp; Koltun, Vladlen; Thuerey, Nils

doi:10.48550/arxiv.2109.15048

Cited by 2 publications

(1 citation statement)

References 24 publications

(34 reference statements)

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“…The convergence in the loss metric suggests that we were able to train a overparameterized neural network with 35 samples of data in 60 epochs. We attribute this to the effect of having so-called 'physical' gradients from training through a PDE solver ( [25]). p .…”

Section: Discovery Of Long-lived Nonlinear Plasma Wavepacketsmentioning

confidence: 99%

Unsupervised Discovery of Inertial-Fusion Plasma Physics using Differentiable Kinetic Simulations and a Maximum Entropy Loss Function

Joglekar¹,

Thomas²

2022

Preprint

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Plasma supports collective modes and particle-wave interactions that leads to complex behavior in, for example, inertial fusion energy applications. While plasma can sometimes be modeled as a charged fluid, a kinetic description is often crucial for studying nonlinear effects in the higher dimensional momentum-position phase-space that describes the full complexity of plasma dynamics. We create a differentiable solver for the 3D partial-differential-equation describing the plasma kinetics and introduce a domain-specific objective function. Using this framework, we perform gradient-based optimization of neural networks that provide forcing function parameters to the differentiable solver given a set of initial conditions. We apply this to an inertial-fusion relevant configuration and find that the optimization process exploits a novel physical effect.

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Section: Discovery Of Long-lived Nonlinear Plasma Wavepacketsmentioning

confidence: 99%

Unsupervised Discovery of Inertial-Fusion Plasma Physics using Differentiable Kinetic Simulations and a Maximum Entropy Loss Function

Joglekar¹,

Thomas²

2022

Preprint

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Potentials and challenges in enhancing the gear transmission development with machine learning methods—a review

Sendlbeck,

Maurer,

Otto

et al. 2023

Forsch Ingenieurwes

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The electrification of vehicle powertrains and the expected engineering labor shortage are ongoing key challenges in the gear transmission development. Because traditional methods reach limits, the solution is further automating the design process while enabling flexible and optimal design solutions even with rapidly changing constraints and requirements. We therefore review the current design process, review state-of-the-art methods for automated gear transmission design, and evaluate their potential and the challenges in combination with using machine learning methods. In focus are grammars and graph grammars in particular, which offer an approach to represent and generate the relational structure of transmission topologies or shaft arrangements. Other potential approaches are knowledge-based engineering, which allows to choose various predefined expert design solution and combine them to new designs, and constraint programming for gear transmission generation. Combining these methods with latest advances in reinforcement learning, machine learning for inverse problem-solving, and graph neural networks offers promising capabilities for automatic topology generation and dimensioning of gear transmissions.

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Physical Gradients for Deep Learning

Cited by 2 publications

References 24 publications

Unsupervised Discovery of Inertial-Fusion Plasma Physics using Differentiable Kinetic Simulations and a Maximum Entropy Loss Function

Unsupervised Discovery of Inertial-Fusion Plasma Physics using Differentiable Kinetic Simulations and a Maximum Entropy Loss Function

Potentials and challenges in enhancing the gear transmission development with machine learning methods—a review

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