arXiv subjects

Susana Lopez-Moreno

Publications and source records attributed to Susana Lopez-Moreno.

8 recordsLinked to original sources

arXiv2026

Adaptive Nonlinear Vector Autoregression: Robust Forecasting for Noisy Chaotic Time Series

Nonlinear vector autoregression (NVAR) and reservoir computing (RC) have shown promise in forecasting chaotic dynamical systems, such as the Lorenz-63 model and El Nino-Southern Oscillation. However, their reliance on fixed nonlinear transformations - polynomial expansions in NVAR or random feature maps in RC - limits their adaptability to high noise or complex real-world data. Furthermore, these methods also exhibit poor scalability in high-dimensional settings due to costly matrix inversion during optimization. We propose a data-adaptive NVAR model that combines delay-embedded linear inputs with features generated by a shallow, trainable multilayer perceptron (MLP). Unlike standard NVAR and RC models, the MLP and linear readout are jointly trained using gradient-based optimization, enabling the model to learn data-driven nonlinearities, while preserving a simple readout structure and improving scalability. Initial experiments across multiple chaotic systems, tested under noise-free and synthetically noisy conditions, showed that the adaptive model outperformed in predictive accuracy the standard NVAR, a leaky echo state network (ESN) - the most common RC model - and a hybrid ESN, thereby showing robust forecasting under noisy conditions.

cs.LG↗

arXiv2026

PCA-Enhanced Adaptive NVAR Framework for High-Resolution Sea Surface Temperature Forecasting in the East Sea

Accurate forecasting of sea surface temperature (SST) is essential for marine ecosystem monitoring, climate assessment, fisheries management, and operational ocean forecasting. While numerical ocean models provide reliable predictions, they are computationally expensive, and conventional machine learning methods often suffer from high-dimensional inputs and error accumulation during long-term autonomous forecasting. This study extends our previously proposed Adaptive Nonlinear Vector Autoregression (Adaptive NVAR) framework to high-resolution real-world SST prediction by integrating Principal Component Analysis (PCA) through Singular Value Decomposition (SVD). Daily SST fields from the GLORYS12V1 reanalysis dataset covering the East Sea, Yellow Sea, and East China Sea are compressed into a lower-dimensional latent representation that preserves the dominant spatial variability. The proposed reduced-order framework is evaluated using autonomous rolling forecasts up to a 90-day horizon and compared with Standard NVAR (Next Generation Reservoir Computing) and a Persistence baseline. Across all three regions, Adaptive NVAR consistently suppresses long-term error accumulation, achieving up to 96.52% improvement in mean squared error relative to Persistence while maintaining stable predictive performance throughout extended forecasting. Although the adaptive architecture incurs a higher one-time offline optimization cost than Standard NVAR, inference is completed in milliseconds, making the proposed framework an efficient and scalable approach for long-term, high-resolution ocean state forecasting.

cs.LG↗

arXiv2026

CheMLFlow: An Open-Source Platform for Cheminformatics and Materials Informatics Applications

CheMLFlow is an open-source platform for building and executing end-to-end, high-throughput, and agentic workflows for scientific and technological applications. CheMLFlow targets a common bottleneck in scientific machine learning development, where researchers often need to assemble data acquisition, curation, representation, model training, validation, screening, interpretation, and reporting into a reproducible pipeline, even when their primary research contribution concerns only one stage. CheMLFlow provides modular workflow components, ready-to-run reference pipelines, standardized artifacts, and evaluation outputs that reduce orchestration overhead and support benchmarking across methods and datasets. The platform is designed to be extensible, reproducible, and automation friendly, with pluggable representations and models, deterministic splits, explicit run artifacts, batch execution, and report generation. As scientific software increasingly moves toward agent assisted experimentation, CheMLFlow's configuration driven workflows and structured outputs also provide a practical interface for coding agents to help users construct experiments, inspect results, and summarize findings under human supervision. This article describes the system architecture, core workflows, and benchmarks that reach literature performance for quantum mechanical, physicochemical and bioactivity property prediction, and use cases involving time series datasets demonstrating applications beyond molecular chemistry datasets.

cs.LG↗

arXiv2026

Hamiltonian and Symplectic Tensors in the T-product Algebra

We study Hamiltonian and symplectic tensor structures in the T-product algebra. We define T-Hamiltonian and T-symplectic tensors and characterize them through their Fourier-domain slices. For T-Hamiltonian tensors we establish the standard block form and the spectral symmetry of T-eigenvalues, while for T-symplectic tensors we derive the inverse and exponential-map properties. Our main result is a constructive T-Williamson normal form for tensors whose Fourier-domain slices are real symmetric positive-definite matrices. We also show that, under the Hermitian symplectic convention adopted here, this decomposition does not extend directly to arbitrary Hermitian positive-definite Fourier-domain slices, and we derive a real-valued recovery criterion under Fourier conjugate symmetry. Numerical experiments verify the construction, exhibit runtime trends consistent with the slice-wise complexity $O(pn^3)$, and illustrate the framework on a Fourier-domain encoding of covariance-matrix families arising in continuous-variable quantum dynamics.

math.NA↗

arXiv2026

Tensor CUR Decomposition under the Linear-Map-Based Tensor-Tensor Multiplication

The factorization of three-dimensional data continues to gain attention due to its relevance in representing and compressing large-scale datasets. The linear-map-based tensor-tensor multiplication is a matrix-mimetic operation that extends the notion of matrix multiplication to higher order tensors, and which is a generalization of the T-product. Under this framework, we introduce the tensor CUR decomposition, show its performance in video foreground-background separation for different linear maps and compare it to a robust matrix CUR decomposition, another tensor approximation and the slice-based singular value decomposition (SS-SVD). We also provide a theoretical analysis of our tensor CUR decomposition, extending classical matrix results to establish exactness conditions and perturbation bounds.

math.NA↗

arXiv2026

Standardization of Post-Publication Code Verification by Journals is Possible with the Support of the Community

Reproducibility remains a challenge in machine learning research. While code and data availability requirements have become increasingly common, post-publication verification in journals is still limited and unformalized. This position paper argues that it is plausible for journals and conference proceedings to implement post-publication verification. We propose a modification to ACM pre-publication verification badges that allows independent researchers to submit post-publication code replications to the journal, leading to visible verification badges included in the article metadata. Each article may earn up to two badges, each linked to verified code in its corresponding public repository. We describe the motivation, related initiatives, a formal framework, the potential impact, possible limitations, and alternative views.

cs.LG↗

arXiv2025

On the computation of tensor functions under tensor-tensor multiplications with linear maps

In this paper we study the computation of both algebraic and non-algebraic tensor functions under the tensor-tensor multiplication with linear maps. In the case of algebraic tensor functions, we prove that the asymptotic exponent of both the tensor-tensor multiplication and the tensor polynomial evaluation problem under this multiplication is the same as that of the matrix multiplication, unless the linear map is injective. As for non-algebraic functions, we define the tensor geometric mean and the tensor Wasserstein mean for pseudo-positive-definite tensors under the tensor-tensor multiplication with invertible linear maps, and we show that the tensor geometric mean can be calculated by solving a specific Riccati tensor equation. Furthermore, we show that the tensor geometric mean does not satisfy the resultantal (determinantal) identity in general, which the matrix geometric mean always satisfies. Then we define a pseudo-SVD for the injective linear map case and we apply it on image data compression.

math.NA↗

arXiv2025

Order Theory in the Context of Machine Learning

The paper ``Tropical Geometry of Deep Neural Networks'' by L. Zhang et al. introduces an equivalence between integer-valued neural networks (IVNN) with $\text{ReLU}_{t}$ and tropical rational functions, which come with a map to polytopes. Here, IVNN refers to a network with integer weights but real biases, and $\text{ReLU}_{t}$ is defined as $\text{ReLU}_{t}(x)=\max(x,t)$ for $t\in\mathbb{R}\cup\{-\infty\}$. For every poset with $n$ points, there exists a corresponding order polytope, i.e., a convex polytope in the unit cube $[0,1]^n$ whose coordinates obey the inequalities of the poset. We study neural networks whose associated polytope is an order polytope. We then explain how posets with four points induce neural networks that can be interpreted as $2\times 2$ convolutional filters. These poset filters can be added to any neural network, not only IVNN. Similarly to maxout, poset pooling filters update the weights of the neural network during backpropagation with more precision than average pooling, max pooling, or mixed pooling, without the need to train extra parameters. We report experiments that support our statements. We also define the structure of algebra over the operad of posets on poset neural networks and tropical polynomials. This formalism allows us to study the composition of poset neural network arquitectures and the effect on their corresponding Newton polytopes, via the introduction of the generalization of two operations on polytopes: the Minkowski sum and the convex envelope.

cs.CV↗