NURBS-Diff: A Differentiable Programming Module for NURBS

Prasad, Anjana Deva; Balu, Aditya; Shah, Harshil; Sarkar, Soumik; Hegde, Chinmay; Krishnamurthy, Adarsh

doi:10.1016/j.cad.2022.103199

Cited by 15 publications

(6 citation statements)

References 10 publications

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“…The NURBS surface is composed of different B-splines. Each point on the NURBS surface is thereby uniquely defined by the set of control points P , control point weights W , knot vectors U and V as follows [49]:…”

Section: Surface Modelmentioning

confidence: 99%

Automatic Heliostat Learning for In-situ Concentrating Solar Power Plant Optimization with Differentiable Ray Tracing

Pargmann,

Ebert,

Quinto

et al. 2024

Preprint

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Concentrating solar power plants (CSPs) are a clean energy source capable of competitive electricity generation even during night time, as well as the production of carbon-neutral fuels, offering a complementary role alongside photovoltaic plants. In CSPs, thousands of mirrors (heliostats) redirect sunlight onto a receiver, potentially generating temperatures exceeding 1000 °C. Practically, such efficient temperatures are never attained. Several unknown, yet operationally crucial parameters, e.g., misalignment in sun-tracking and surface deformations can cause dangerous temperature spikes, necessitating high safety margins. For competitive levelized cost of energy and large scale deployment, in-situ error measurements are an essential, yet unattained factor. To tackle this, we introduce a differentiable ray tracing machine learning approach that can derive the irradiance distribution of heliostats in a data-driven manner from a small number of calibration images already collected in most solar thermal power plants. By applying gradient-based optimization and a learning NURBS heliostat model, our approach is able to determine sub-millimeter imperfections in a real-world setting and predict heliostat-specific irradiance profiles, exceeding the precision of the state-of-the-art and establishing full automatization. The new optimization pipeline enables concurrent training of physical and data-driven models, representing a pioneering effort in unifying both paradigms for CSPs and can be a blueprint for other domains.

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Section: Surface Modelmentioning

confidence: 99%

Automatic Heliostat Learning for In-situ Concentrating Solar Power Plant Optimization with Differentiable Ray Tracing

Pargmann,

Ebert,

Quinto

et al. 2024

Preprint

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“…Splines have long been used to model surfaces and curves in geometry [19], [20], [21], [22]. Moreover, differentiable splines with parameters that can be fitted using automatic differentiation have also been developed [23]. Recently deep learning methods called neural fields or implicit neural networks have proven to be extremely good and efficient continuous representations [24].…”

Section: B Related Workmentioning

confidence: 99%

“…It has recently been shown that automatic differentiation can be used to learn spline parameters [23]. Hence, we develop differentiable spline representations and use gradient-based optimization to learn the NURBS parameters φ and their input measurement coordinates.…”

Section: Measurement Representationsmentioning

confidence: 99%

“…The knot vector for the view angle dimension has (J + d Θ + 1) elements which are arranged in ascending order. We design its uth element, k u , to be zero when 0 ≤ u < d Θ + 1, uniformly spaced between zero and one when d Θ + 1 ≤ u ≤ J, and one when J < u ≤ J + d Θ [23]. The knot vector for the detector location dimension has (J + d T + 1) elements and is made in a similar manner by using its degree d T .…”

Section: Appendix C Additional Spline Informationmentioning

confidence: 99%

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Differentiable Uncalibrated Imaging

Gupta,

Kothari,

Debarnot

et al. 2024

IEEE Trans. Comput. Imaging

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We propose a differentiable imaging framework to address uncertainty in measurement coordinates such as sensor locations and projection angles. We formulate the problem as measurement interpolation at unknown nodes supervised through the forward operator. To solve it we apply implicit neural networks, also known as neural fields, which are naturally differentiable with respect to the input coordinates. We also develop differentiable spline interpolators which perform as well as neural networks, require less time to optimize and have well-understood properties. Differentiability is key as it allows us to jointly fit a measurement representation, optimize over the uncertain measurement coordinates, and perform image reconstruction which in turn ensures consistent calibration. We apply our approach to 2D and 3D computed tomography, and show that it produces improved reconstructions compared to baselines that do not account for the lack of calibration. The flexibility of the proposed framework makes it easy to extend to almost arbitrary imaging problems.1 We denote by L 2 (M) the space of square integrable functions on M.

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“…A NURBS surface is composed of different B-spline functions and their weighted control points. Each point on the NURBS surface is thereby uniquely defined by a set of points P (control points), W (weights), U , and V (knot vectors), often expressed as [29]:…”

Section: Heliostat Modelmentioning

confidence: 99%

In-Situ Solar Tower Power Plant Optimization by Differentiable Ray Tracing

Pargmann¹,

Ebert²,

Quinto

et al. 2023

Preprint

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Solar tower power plants play a key role to facilitate the ongoing energy transition as they deliver climate neutral electricity and direct heat for chemical processes. These plants generate temperatures over 1000 °C by reflecting sunlight with thousands of mirrors (heliostats) to a receiver. The temper- ature achievable in practice is limited due to the system’s susceptibility to small surface defects and misalignments of individual mirrors, hindering the plant’s full efficiency. We present an inverse render- ing technique that predicts the incident power distribution of each heliostat, including the inaccuracies, based solely on focal spot images that are already acquired in most solar power plants. The method allows reconstructing flawed mirror shapes within sub-mm precision. Applied at the solar tower plant in Juelich, our approach outperforms all alternatives in accuracy and reliability. Our data-driven method is a key ingredient to building digital twins of solar power plants. It can be integrated into the existing infrastructure and plant control at low cost, leading to increased efficiency of existing and decreased expenses for future power plants, the key factors of success in the competitive market. For other fields, our approach can be a blueprint, as we present the option for the very first large-scale indus- trial deployment of differentiable ray tracing. Merging data-intensive Machine Learning with physical modeling creates flexible, data-efficient and trustworthy solutions applicable in science and industry.

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NURBS-Diff: A Differentiable Programming Module for NURBS

Cited by 15 publications

References 10 publications

Automatic Heliostat Learning for In-situ Concentrating Solar Power Plant Optimization with Differentiable Ray Tracing

Automatic Heliostat Learning for In-situ Concentrating Solar Power Plant Optimization with Differentiable Ray Tracing

Differentiable Uncalibrated Imaging

In-Situ Solar Tower Power Plant Optimization by Differentiable Ray Tracing

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