arXiv subjects

Juan Diego Draxl Giannoni

Publications and source records attributed to Juan Diego Draxl Giannoni.

3 recordsLinked to original sources

arXiv2026

Structure-preserving Lift & Learn: Scientific machine learning for nonlinear conservative partial differential equations

This work presents structure-preserving Lift & Learn, a scientific machine learning method that employs lifting variable transformations to learn structure-preserving reduced-order models for nonlinear partial differential equations (PDEs) with conservation laws. We propose a hybrid learning approach based on a recently developed energy-quadratization strategy that uses knowledge of the nonlinearity at the PDE level to derive an equivalent quadratic lifted system with quadratic system energy. The lifted dynamics obtained via energy quadratization are linear in the old variables, making model learning very effective in the lifted setting. Based on the lifted quadratic PDE model form, the proposed method derives quadratic reduced terms analytically and then uses those derived terms to formulate a constrained optimization problem to learn the remaining linear reduced operators in a structure-preserving way. The proposed hybrid learning approach yields computationally efficient quadratic reduced-order models that respect the underlying physics of the high-dimensional problem. We demonstrate the generalizability of quadratic models learned via the proposed structure-preserving Lift & Learn method through three numerical examples: the one-dimensional wave equation with exponential nonlinearity, the two-dimensional sine-Gordon equation, and the two-dimensional Klein-Gordon-Zakharov equations. The numerical results show that the proposed learning approach is competitive with the state-of-the-art structure-preserving data-driven model reduction method in terms of both accuracy and computational efficiency.

cs.LG↗

arXiv2025

Identifying and Characterizing Very Low Mass Spectral Blend Binaries with Machine Learning Methods

We present an approach to identifying and characterizing unresolved, very low mass spectral blend binaries composed of late-M, L, and T dwarfs using machine learning methodologies. We generated and evaluated a series of hierarchical random forest models to distinguish spectral blends from single very low-mass dwarfs, and to classify their primary and secondary components. Models were trained on a sample of single and synthesized binary templates generated from empirical spectra. We explored various aspects of the design of our models, and find that models trained on a full range of single and binary combinations have the best performance for identification and component classification. These models achieve binary identification recall and precision of $\gtrsim$85%, median component classification errors of $\lesssim$0.1 subtypes, and systematic classification uncertainties of $\lesssim$1 subtype, outperforming index-based methods in terms of fidelity, range, and speed. Optimal performance is achieved for binaries composed of L and T dwarf primaries and late-L and T dwarf secondaries. When applied to the spectra of previously confirmed very low-mass binaries, model performance is degraded due to the prevalence of systems with similar component types, but remains high in the optimal performance range. We propose potential improvements to these models, which can be used to explore binary populations among the thousands to millions of very low-mass stars and brown dwarfs anticipated with large-scale spectral surveys such as SPHEREx and Euclid.

astro-ph.SR↗

arXiv2025

Nonlinear energy-preserving model reduction with lifting transformations that quadratize the energy

Existing model reduction techniques for high-dimensional models of conservative partial differential equations (PDEs) encounter computational bottlenecks when dealing with systems featuring non-polynomial nonlinearities. This work presents a nonlinear model reduction method that employs lifting variable transformations to derive structure-preserving quadratic reduced-order models for conservative PDEs with general nonlinearities. We present an energy-quadratization strategy that defines the auxiliary variable in terms of the nonlinear term in the energy expression to derive an equivalent quadratic lifted system with quadratic system energy. The proposed strategy combined with proper orthogonal decomposition model reduction yields quadratic reduced-order models that conserve the quadratized lifted energy exactly in high dimensions. We demonstrate the proposed model reduction approach on four nonlinear conservative PDEs: the one-dimensional wave equation with exponential nonlinearity, the two-dimensional sine-Gordon equation, the two-dimensional Klein-Gordon equation with parametric dependence, and the two-dimensional Klein-Gordon-Zakharov equations. The numerical results show that the proposed lifting approach is competitive with the state-of-the-art structure-preserving hyper-reduction method in terms of both accuracy and computational efficiency in the online stage while providing significant computational gains in the offline stage.

math.NA↗