arXiv subjects

Marina Spivak

Publications and source records attributed to Marina Spivak.

4 recordsLinked to original sources

arXiv2025

Diffusion for Fusion: Designing Stellarators with Generative AI

Stellarators are a prospective class of fusion-based power plants that confine a hot plasma with three-dimensional magnetic fields. Typically framed as a PDE-constrained optimization problem, stellarator design is a time-consuming process that can take hours to solve on a computing cluster. Developing fast methods for designing stellarators is crucial for advancing fusion research. Given the recent development of large datasets of optimized stellarators, machine learning approaches have emerged as a potential candidate. Motivated by this, we present an open inverse problem to the machine learning community: to rapidly generate high-quality stellarator designs which have a set of desirable characteristics. As a case study in the problem space, we train a conditional diffusion model on data from the QUASR database to generate quasisymmetric stellarator designs with desirable characteristics (aspect ratio and mean rotational transform). The diffusion model is applied to design stellarators with characteristics not seen during training. We provide evaluation protocols and show that many of the generated stellarators exhibit solid performance: less than 5% deviation from quasisymmetry and the target characteristics. The modest deviation from quasisymmetry highlights an opportunity to reach the sub 1% target. Beyond the case study, we share multiple promising avenues for generative modeling to advance stellarator design.

cs.LG↗

arXiv2025

A comprehensive exploration of quasisymmetric stellarators and their coil sets

We augment the `QUAsi-symmetric Stellarator Repository' (QUASR) to include vacuum field stellarators with quasihelical symmetry using a globalized optimization workflow. The database now has almost 370,000 quasisaxisymmetry and quasihelically symmetric devices along with coil sets, optimized for a variety of aspect ratios, rotational transforms, and discrete rotational symmetries. This paper outlines a couple of ways to explore and characterize the data set. We plot devices on a near-axis quasisymmetry landscape, revealing close correspondence to this predicted landscape. We also use principal component analysis to reduce the dimensionality of the data so that it can easily be visualized in two or three dimensions. Principal component analysis also gives a mechanism to compare the new devices here to previously published ones in the literature. We are able to characterize the structure of the data, observe clusters, and visualize the progression of devices in these clusters. The topology of the data is governed by the interplay of the design constraints and valleys of the quasisymmetry objective. These techniques reveal that the data has structure, and that typically one, two or three principal components are sufficient to characterize it. The latest version of QUASR is archived at https://zenodo.org/doi/10.5281/zenodo.10050655 and can be explored online at quasr.flatironinstitute.org.

physics.app-ph↗

arXiv2019

Factorization of the translation kernel for fast rigid image alignment

An important component of many image alignment methods is the calculation of inner products (correlations) between an image of $n\times n$ pixels and another image translated by some shift and rotated by some angle. For robust alignment of an image pair, the number of considered shifts and angles is typically high, thus the inner product calculation becomes a bottleneck. Existing methods, based on fast Fourier transforms (FFTs), compute all such inner products with computational complexity $\mathcal{O}(n^3 \log n)$ per image pair, which is reduced to $\mathcal{O}(N n^2)$ if only $N$ distinct shifts are needed. We propose to use a factorization of the translation kernel (FTK), an optimal interpolation method which represents images in a Fourier--Bessel basis and uses a rank-$H$ approximation of the translation kernel via an operator singular value decomposition (SVD). Its complexity is $\mathcal{O}(Hn(n + N))$ per image pair. We prove that $H = \mathcal{O}((W + \log(1/ε))^2)$, where $2W$ is the magnitude of the maximum desired shift in pixels and $ε$ is the desired accuracy. For fixed $W$ this leads to an acceleration when $N$ is large, such as when sub-pixel shift grids are considered. Finally, we present numerical results in an electron cryomicroscopy application showing speedup factors of $3$-$10$ with respect to the state of the art.

math.NA↗

arXiv2017

Rapid solution of the cryo-EM reconstruction problem by frequency marching

Determining the three-dimensional structure of proteins and protein complexes at atomic resolution is a fundamental task in structural biology. Over the last decade, remarkable progress has been made using "single particle" cryo-electron microscopy (cryo-EM) for this purpose. In cryo-EM, hundreds of thousands of two-dimensional images are obtained of individual copies of the same particle, each held in a thin sheet of ice at some unknown orientation. Each image corresponds to the noisy projection of the particle's electron-scattering density. The reconstruction of a high-resolution image from this data is typically formulated as a nonlinear, non-convex optimization problem for unknowns which encode the angular pose and lateral offset of each particle. Since there are hundreds of thousands of such parameters, this leads to a very CPU-intensive task---limiting both the number of particle images which can be processed and the number of independent reconstructions which can be carried out for the purpose of statistical validation. Here, we propose a deterministic method for high-resolution reconstruction that operates in an ab initio manner---that is, without the need for an initial guess. It requires a predictable and relatively modest amount of computational effort, by marching out radially in the Fourier domain from low to high frequency, increasing the resolution by a fixed increment at each step.

math.NA↗