arXiv subjects

Arnur Nigmetov

Publications and source records attributed to Arnur Nigmetov.

13 recordsLinked to original sources

arXiv2026

Joint Estimation of Properties of the Lunar Subsurface and Galactic Foregrounds with LuSEE-Night

The Lunar Surface Electromagnetics Experiment (LuSEE-Night) is a joint NASA-DOE-ESA low-frequency radio telescope that will reach the lunar far side in 2027. The unknown dielectric properties of the subsurface at the LuSEE-Night landing site impose the most significant limitation for precision instrument calibration, as reflections from the lunar subsurface can change the primary beam at the 10-20% level. Simulations of these effects have provided insight and concern, showing that the lunar subsurface modeled as a lossy dielectric can absorb a large amount of the power of the sky signal. While this absorption may not strongly impact the signal-to-noise ratio in a sky-noise-dominated regime, it could complicate the beam pattern and make the signal more difficult to model and interpret. We have simulated the far-field properties of the LuSEE-Night beam for varying dielectric profiles of the lunar subsurface. We find that varying the properties of the lunar subsurface has the most significant impact around the antenna resonance, impacting its amplitude, position and width. Conversely, changing the properties of the foreground impacts the data across the band. We use a Bayesian inference pipeline to jointly estimate parameters of a galactic foreground model and dielectric properties of the lunar subsurface around the LuSEE-Night landing site and find that parameters of both the galaxy and subsurface properties can be estimated jointly. While the modeling is somewhat idealized, we believe that the results are largely robust owing to the fact that spectral variations for plausible subsurface and galaxy models have very different spectral signatures.

astro-ph.IM↗

arXiv2026

Persistence-Augmented Neural Networks

Topological Data Analysis (TDA) provides tools to describe the shape of data, but integrating topological features into deep learning pipelines remains challenging, especially when preserving local geometric structure rather than summarizing it globally. We propose a persistence-based data augmentation framework that encodes local gradient flow regions and their hierarchical evolution using the Morse-Smale complex. This representation, compatible with both convolutional and graph neural networks, retains spatially localized topological information across multiple scales. Importantly, the augmentation procedure itself is efficient, with computational complexity $O(n \log n)$, making it practical for large datasets. We evaluate our method on histopathology image classification and 3D porous material regression, where it consistently outperforms baselines and global TDA descriptors such as persistence images and landscapes. We also show that pruning the base level of the hierarchy reduces memory usage while maintaining competitive performance. These results highlight the potential of local, structured topological augmentation for scalable and interpretable learning across data modalities.

cs.LG↗

arXiv2026

On Neural Scaling Laws for Weather Emulation through Continual Training

Neural scaling laws, which in some domains can predict the performance of large neural networks as a function of model, data, and compute scale, are the cornerstone of building foundation models in Natural Language Processing and Computer Vision. We study neural scaling in Scientific Machine Learning, focusing on models for weather forecasting. To analyze scaling behavior in as simple a setting as possible, we adopt a minimal, scalable, general-purpose Swin Transformer architecture, and we use continual training with constant learning rates and periodic cooldowns as an efficient training strategy. We show that models trained in this minimalist way follow predictable scaling trends and even outperform standard cosine learning rate schedules. Cooldown phases can be re-purposed to improve downstream performance, e.g., enabling accurate multi-step rollouts over longer forecast horizons as well as sharper predictions through spectral loss adjustments. We also systematically explore a wide range of model and dataset sizes under various compute budgets to construct IsoFLOP curves, and we identify compute-optimal training regimes. Extrapolating these trends to larger scales highlights potential performance limits, demonstrating that neural scaling can serve as an important diagnostic for efficient resource allocation. We open-source our code for reproducibility.

cs.LG↗

arXiv2025

Topological potentials guiding protein self-assembly

The simulated self-assembly of molecular building blocks into functional complexes is a key area of study in computational biology and materials science. Self-assembly simulations of proteins using physically-motivated potentials for non-polar interactions, can identify the biologically correct assembly as the energy-minimizing state. Short-range potentials, however, produce rugged energy landscapes, which lead to simulations becoming trapped in non-functional local minimizers. Successful self-assembly simulations depend on the physical realism of the driving potentials as well as their ability to efficiently explore the configuration space. We introduce a long-range topological potential, quantified via weighted total persistence, and combine it with the morphometric approach to solvation-free energy. This combination improves the assembly success rate in simulations of the tobacco mosaic virus dimer and other protein complexes by up to sixteen-fold compared with the morphometric model alone. It further enables successful simulation in systems that don't otherwise assemble during the examined timescales. Compared to previous topology-based work, which has been primarily descriptive, our approach uses topological measures as an active energetic bias that is independent of electrostatics or chemical specificity and depends only on atomic coordinates. Therefore, the method can, in principle, be applied to arbitrary systems where such coordinates are optimized. Integrating topological descriptions into an energy function offers a general strategy for overcoming kinetic barriers in molecular simulations, with potential applications in drug design, materials development, and the study of complex self-assembly processes.

cond-mat.soft↗

arXiv2024

Distributed Computation of Persistent Cohomology

Persistent (co)homology is a central construction in topological data analysis, where it is used to quantify prominence of features in data to produce stable descriptors suitable for downstream analysis. Persistence is challenging to compute in parallel because it relies on global connectivity of the data. We propose a new algorithm to compute persistent cohomology in the distributed setting. It combines domain and range partitioning. The former is used to reduce and sparsify the coboundary matrix locally. After this initial local reduction, we redistribute the matrix across processors for the global reduction. We experimentally compare our cohomology algorithm with DIPHA, the only publicly available code for distributed computation of persistent (co)homology; our algorithm demonstrates a significant improvement in strong scaling.

cs.CG↗

arXiv2024

Wilkins: HPC In Situ Workflows Made Easy

In situ approaches can accelerate the pace of scientific discoveries by allowing scientists to perform data analysis at simulation time. Current in situ workflow systems, however, face challenges in handling the growing complexity and diverse computational requirements of scientific tasks. In this work, we present Wilkins, an in situ workflow system that is designed for ease-of-use while providing scalable and efficient execution of workflow tasks. Wilkins provides a flexible workflow description interface, employs a high-performance data transport layer based on HDF5, and supports tasks with disparate data rates by providing a flow control mechanism. Wilkins seamlessly couples scientific tasks that already use HDF5, without requiring task code modifications. We demonstrate the above features using both synthetic benchmarks and two science use cases in materials science and cosmology.

cs.DC↗

arXiv2023

Topological Optimization with Big Steps

Using persistent homology to guide optimization has emerged as a novel application of topological data analysis. Existing methods treat persistence calculation as a black box and backpropagate gradients only onto the simplices involved in particular pairs. We show how the cycles and chains used in the persistence calculation can be used to prescribe gradients to larger subsets of the domain. In particular, we show that in a special case, which serves as a building block for general losses, the problem can be solved exactly in linear time. This relies on another contribution of this paper, which eliminates the need to examine a factorial number of permutations of simplices with the same value. We present empirical experiments that show the practical benefits of our algorithm: the number of steps required for the optimization is reduced by an order of magnitude.

cs.CG↗

arXiv2023

Robustifying State-space Models for Long Sequences via Approximate Diagonalization

State-space models (SSMs) have recently emerged as a framework for learning long-range sequence tasks. An example is the structured state-space sequence (S4) layer, which uses the diagonal-plus-low-rank structure of the HiPPO initialization framework. However, the complicated structure of the S4 layer poses challenges; and, in an effort to address these challenges, models such as S4D and S5 have considered a purely diagonal structure. This choice simplifies the implementation, improves computational efficiency, and allows channel communication. However, diagonalizing the HiPPO framework is itself an ill-posed problem. In this paper, we propose a general solution for this and related ill-posed diagonalization problems in machine learning. We introduce a generic, backward-stable "perturb-then-diagonalize" (PTD) methodology, which is based on the pseudospectral theory of non-normal operators, and which may be interpreted as the approximate diagonalization of the non-normal matrices defining SSMs. Based on this, we introduce the S4-PTD and S5-PTD models. Through theoretical analysis of the transfer functions of different initialization schemes, we demonstrate that the S4-PTD/S5-PTD initialization strongly converges to the HiPPO framework, while the S4D/S5 initialization only achieves weak convergences. As a result, our new models show resilience to Fourier-mode noise-perturbed inputs, a crucial property not achieved by the S4D/S5 models. In addition to improved robustness, our S5-PTD model averages 87.6% accuracy on the Long-Range Arena benchmark, demonstrating that the PTD methodology helps to improve the accuracy of deep learning models.

cs.LG↗

arXiv2023

Fast Merge Tree Computation via SYCL

A merge tree is a topological descriptor of a real-valued function. Merge trees are used in visualization and topological data analysis, either directly or as a means to another end: computing a 0-dimensional persistence diagram, identifying connected components, performing topological simplification, etc. Scientific computing relies more and more on GPUs to achieve fast, scalable computation. For efficiency, data analysis should take place at the same location as the main computation, which motivates interest in parallel algorithms and portable software for merge trees that can run not only on a CPU, but also on a GPU, or other types of accelerators. The SYCL standard defines a programming model that allows the same code, written in standard C++, to compile targets for multiple parallel backends (CPUs via OpenMP or TBB, NVIDIA GPUs via CUDA, AMD GPUs via ROCm, Intel GPUs via Level Zero, FPGAs). In this paper, we adapt the triplet merge tree algorithm to SYCL and compare our implementation with the VTK-m implementation, which is the only other implementation of merge trees for GPUs that we know of.

cs.CG↗

arXiv2020

Topological Regularization via Persistence-Sensitive Optimization

Optimization, a key tool in machine learning and statistics, relies on regularization to reduce overfitting. Traditional regularization methods control a norm of the solution to ensure its smoothness. Recently, topological methods have emerged as a way to provide a more precise and expressive control over the solution, relying on persistent homology to quantify and reduce its roughness. All such existing techniques back-propagate gradients through the persistence diagram, which is a summary of the topological features of a function. Their downside is that they provide information only at the critical points of the function. We propose a method that instead builds on persistence-sensitive simplification and translates the required changes to the persistence diagram into changes on large subsets of the domain, including both critical and regular points. This approach enables a faster and more precise topological regularization, the benefits of which we illustrate with experimental evidence.

cs.LG↗

arXiv2020

Efficient Approximation of the Matching Distance for 2-parameter persistence

The matching distance is a computationally tractable topological measure to compare multi-filtered simplicial complexes. We design efficient algorithms for approximating the matching distance of two bi-filtered complexes to any desired precision $ε>0$. Our approach is based on a quad-tree refinement strategy introduced by Biasotti et al., but we recast their approach entirely in geometric terms. This point of view leads to several novel observations resulting in a practically faster algorithm. We demonstrate this speed-up by experimental comparison and provide our code in a public repository which provides the first efficient publicly available implementation of the matching distance.

cs.CG↗

arXiv2019

Metric Spaces with Expensive Distances

In algorithms for finite metric spaces, it is common to assume that the distance between two points can be computed in constant time, and complexity bounds are expressed only in terms of the number of points of the metric space. We introduce a different model where we assume that the computation of a single distance is an expensive operation and consequently, the goal is to minimize the number of such distance queries. This model is motivated by metric spaces that appear in the context of topological data analysis. We consider two standard operations on metric spaces, namely the construction of a $1+\varepsilon$-spanner and the computation of an approximate nearest neighbor for a given query point. In both cases, we partially explore the metric space through distance queries and infer lower and upper bounds for yet unexplored distances through triangle inequality. For spanners, we evaluate several exploration strategies through extensive experimental evaluation. For approximate nearest neighbors, we prove that our strategy returns an approximate nearest neighbor after a logarithmic number of distance queries.

cs.CG↗

arXiv2016

Geometry Helps to Compare Persistence Diagrams

Exploiting geometric structure to improve the asymptotic complexity of discrete assignment problems is a well-studied subject. In contrast, the practical advantages of using geometry for such problems have not been explored. We implement geometric variants of the Hopcroft--Karp algorithm for bottleneck matching (based on previous work by Efrat el al.) and of the auction algorithm by Bertsekas for Wasserstein distance computation. Both implementations use k-d trees to replace a linear scan with a geometric proximity query. Our interest in this problem stems from the desire to compute distances between persistence diagrams, a problem that comes up frequently in topological data analysis. We show that our geometric matching algorithms lead to a substantial performance gain, both in running time and in memory consumption, over their purely combinatorial counterparts. Moreover, our implementation significantly outperforms the only other implementation available for comparing persistence diagrams.

cs.CG↗