arXiv subjects

Jose Miguel Lara Rangel

Publications and source records attributed to Jose Miguel Lara Rangel.

3 recordsLinked to original sources

arXiv2026

Beyond Time Induction: Structured Conditional Neural Solvers for Parametric Stochastic-Volatility Pricing

Physics-informed neural networks provide a flexible framework for learning parametric PDE solution families without labeled data, yet preserving accurate derivatives across heterogeneous regimes remains challenging. Structured neural solvers offer compact representations, but restrictive conditional parameterizations can limit adaptation across the solution family. We introduce BeTINN, a structured conditional architecture extending time-induced modulation through multi-directional time-parameter conditioning and a joint residual pathway. We evaluate BeTINN on the Heston stochastic-volatility PDE, a demanding parametric problem with mixed derivatives and economically relevant first- and second-order sensitivities. BeTINN improves joint accuracy across normalized option value and key sensitivity metrics relative to our baselines. Controlled ablations characterize the roles of its architectural components. We further find that validation physics loss is informative but does not fully determine differential fidelity, and that accurate solution values can coexist with localized derivative errors. These results support structured conditional adaptation and motivate derivative-aware evaluation when sensitivities are downstream quantities of interest.

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arXiv2026

SPDEBench: An Extensive Benchmark for Learning Stochastic PDEs

Stochastic Partial Differential Equations (SPDEs) driven by random noise play a central role in modeling physical processes with rough spatio-temporal dynamics, such as turbulence flows, superconductors, and quantum dynamics. Although machine learning (ML)-based surrogate models have shown promise for efficiently approximating such dynamics, progress remains limited by the lack of a unified benchmark with controlled data generation and comprehensive evaluation. This gap is particularly significant for singular SPDEs, for which benchmark datasets are largely unavailable and reliable simulation requires numerically delicate schemes based on renormalization. Moreover, subtle differences in data-generation procedures, such as noise approximation, basis choice, and the inclusion of renormalization, can significantly affect the resulting datasets and, consequently, model evaluation. We introduce SPDEBench, the first unified benchmark for ML-based SPDE learning. SPDEBench provides ready-to-use datasets for physically and mathematically significant SPDEs on 1-3D domains with periodic or Dirichlet boundary condition. Both regular and singular SPDEs are taken into consideration. SPDEBench also incorporates representative ML baselines in operator learning, together with 7 evaluation metrics, including Sobolev and distributional metrics beyond the standard $L^2$-error. Supported by SPDEBench, we conduct systematic evaluations of model accuracy, robustness, and out-of-distribution generalization under controlled data variations. Our numerical results show that SPDE-aware architectures generally achieve stronger performance than generic operator-learning baselines. These findings establish SPDEBench as a reproducible and extensible resource, paving pathway for principled benchmarking and architecture design for stochastic spatio-temporal dynamics.

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arXiv2024

Learning to Forget using Hypernetworks

Machine unlearning is gaining increasing attention as a way to remove adversarial data poisoning attacks from already trained models and to comply with privacy and AI regulations. The objective is to unlearn the effect of undesired data from a trained model while maintaining performance on the remaining data. This paper introduces HyperForget, a novel machine unlearning framework that leverages hypernetworks - neural networks that generate parameters for other networks - to dynamically sample models that lack knowledge of targeted data while preserving essential capabilities. Leveraging diffusion models, we implement two Diffusion HyperForget Networks and used them to sample unlearned models in Proof-of-Concept experiments. The unlearned models obtained zero accuracy on the forget set, while preserving good accuracy on the retain sets, highlighting the potential of HyperForget for dynamic targeted data removal and a promising direction for developing adaptive machine unlearning algorithms.

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