arXiv subjects

Mauro Valorani

Publications and source records attributed to Mauro Valorani.

4 recordsLinked to original sources

arXiv2026

A C++ implementation of the G-Scheme stiff ODE solver with multi-resolution sparse hash-table kernel lookup

The G-Scheme is an explicit, adaptive integration framework for stiff systems of ordinary differential equations that exploits a local time-scale decomposition provided by the eigensystem of the Jacobian (the kernel set). Its computational cost is dominated by the evaluation of a new kernel set at each time step. In a recent paper [R.Malpica Galassi and M.Valorani, Combust. Theory Model. 2025], we introduced a multi-resolution sparse hash-table strategy that replaces online kernel computation with retrieval from a precomputed lookup table, demonstrated in Python. Here we present cpp-gscheme, a production-grade C++ implementation of both the G-Scheme and the multi-resolution hash table, together with the porting methodology that guarantees behavioural equivalence with the Python reference: identical scaling, binning and hashing semantics, a bitwise-inert retrieval hook in the integrator, and a fully native evaluation path for the chemical source terms. On 33 n-heptane autoignition mechanisms spanning 56-459 species plus the detailed 654-species mechanism, the hash-tabulated C++ G-Scheme retrieves 100 percent of the kernel sets, performs zero online eigen decompositions, and outperforms the natively compiled CVODE solver by a factor increasing from 2.7x (56 species) to 9.3x (654 species), with observed cost scaling of approximately N power 1.4 versus CVODE's N power 1.9. A three-metric accuracy assessment (ignition delay, equilibrium state, and accumulated entropy-progress error) shows that the solver contributes negligibly to the overall error budget, which is dominated by skeletal reduction. Consequently, a 5 percent ignition-delay target is achieved by the 80-species skeletal mechanism with a 225x speed-up over CVODE on the detailed mechanism. The software, training-set builders, and benchmark drivers are released as open source.

math-ph↗

arXiv2026

The Algebra of Units: From Buckingham's Pi-grec Theorem to Latent-Variable Learning

Engineers often measure many quantities-speed, pressure, temperature, length-expressed in different physical units. The Buckingham Pi-grec theorem states that these variables can always be combined into a smaller set of dimensionless numbers whose values fully determine the system's behaviour. Identifying the appropriate dimensionless groups has traditionally required expert knowledge and physical insight. This paper shows that they can instead be discovered automatically from data, without prior knowledge of the governing physics. The key observation is that, after logarithmic transformation, measurements collected under different scalings of the same system lie on a low-dimensional manifold whose geometry is determined by the underlying dimensionless groups. Singular value decomposition (SVD) identifies this manifold directly from data. A subsequent search over integer-exponent combinations recovers candidate dimensionless quantities, while a repeating-variable filter retains only those constructed from the machine's characteristic scales. This procedure recovers familiar engineering groups, including the flow coefficient, head coefficient, and Mach number, while excluding equivalent but less interpretable alternatives. The method is demonstrated on a synthetic compressor dataset containing 16,000 measurements. Starting from raw dimensional variables and no physics input, it recovers the correct dimensionless groups to numerical precision and reproduces the compressor performance map with an error below 0.01%. More broadly, the work reveals a close connection between classical dimensional analysis and modern data-driven learning. Both rely on the same underlying algebraic structure, suggesting new approaches for building physical models that are simultaneously interpretable, scalable, and data-efficient.

math-ph↗

arXiv2026

Learning Stiff Dynamical Operators: Scaling, Fast-Slow Excitation, and Eigen-Consistent Neural Models

Stiff dynamical systems represent a central challenge in multi scale modeling across combustion, chemical kinetics, and nonlinear dynamical systems. Neural operator learning has recently emerged as a promising approach to approximate dynamical generators from data, yet stiffness imposes severe obstacles: training errors concentrate on slow manifold states, collapse of fast dynamics occurs, and the learned operator may fail to reproduce the true eigenstructure. We demonstrate three key advances enabling accurate learning of stiff operators and preserving spectral fidelity: (i) stiffness aware scaling of time derivatives, (ii) fast direction excitation via local trajectory cloud bursts, and (iii) autograd-based Jacobian diagnostics ensuring eigenstructure fidelity. Applied to the Davis-Skodje system, the approach recovers both slow and fast modes across stiffness regimes, reducing fast eigenvalue error by an order of magnitude while improving rollout fidelity. These results argue that spectral fidelity - not trajectory accuracy alone - should be a first-class target in data driven learning of stiff operators.

physics.comp-ph↗

arXiv2016

Detached eddy simulation of shock unsteadiness in an over-expanded planar nozzle

This work investigates the self-excited shock wave oscillations in a three-dimensional planar over-expanded nozzle turbulent flow by means of Detached Eddy Simulations. Time resolved wall pressure measurements are used as primary diagnostics. The statistical analysis reveals that the shock unsteadiness has common features in terms of the root mean square of the pressure fluctuations with other classical shock wave/boundary layer interactions, like compression ramps and incident shocks on a flat plate. The Fourier transform and the continuous wavelet transform are used to conduct the spectral analysis. The results of the former indicate that the pressure in the shock region is characterized by a broad low-frequency content, without any resonant tone. The wavelet analysis, which is well suited to study non stationary process, reveals that the pressure signal is characterized by an amplitude and a frequency modulation in time.

physics.flu-dyn↗