arXiv subjects

Gustaaf Jacobs

Publications and source records attributed to Gustaaf Jacobs.

5 recordsLinked to original sources

arXiv2026

Learning hidden-state dynamics from unpaired snapshots with lift-project SDEs

Many systems are observed only through unpaired snapshots, with population samples available at each time point but no correspondence between samples at different times. These snapshots determine the one-time distributions but leave the temporal coupling unspecified, requiring a modeling prior to connect successive times. We propose the lift-project stochastic differential equation (SDE), an autonomous SDE on the observed coordinate and a few hidden coordinates, trained only to match the snapshots. Most existing methods, including time-dependent SDEs, Schrödinger bridges and optimal transport, evolve the observed coordinate alone. For a scalar observation, the classical comparison theorem implies that all such models have non-negative lagged covariance, so on data whose lagged covariance turns negative, their error has a computable floor. The lift-project SDE is not bound by this floor. On two representative partially observed systems, the Duffing and pendulum oscillators, at comparable fit to the snapshots, the proposed method reduces the lagged-covariance error by factors of 2.4 and 6.6 relative to the strongest baseline and is the only model below the error floor; one hidden coordinate is already enough for such improvement. Furthermore, if a second experiment changes only the initial state of the hidden coordinate, no single model that evolves the observed coordinate alone can fit both experiments, whereas a single lift-project SDE can.

cs.LG↗

arXiv2026

Neural-Network and Reduced-order Modeling Workflows for AI-Driven CFD: Fast Response Surfaces, Reduced Dynamics and Jet in Cross-flow Examples

Highly resolved computational fluid dynamics (CFD) simulations are essential for design but too expensive for dense design-space sampling. This chapter presents an AI-driven CFD workflow that combines scalar-response modeling and reduced-order dynamics using jet-in-cross-flow examples. A reacting hydrogen jet-in-cross-flow study is first used to train a multilayer perceptron (MLP) mapping injector spacing to unburnt hydrogen throughput, wall heat transfer, and bulk temperature concentration, with shape-preserving interpolation as a baseline. The CFD samples show a non-monotonic spacing response, and the MLP identifies an intermediate-to-wide favorable region near eight jet diameters. Leave-one-sample-out validation shows strong dependence on the predicted quantity: the bulk temperature concentration is robust, while heat transfer and unburnt hydrogen throughput are substantially harder to predict. Sparse Identification of Nonlinear Dynamics (SINDy) is then used as a reduced-order modeling framework for field-derived Reynolds-stress statistics. The parametric SINDy model provides compact field-level predictions at simulated and out-of-sample spacings, though its aggregate spacing-mean Reynolds-stress error is $6.7\%$ higher than the POD-basis reconstruction because of degradation at selected cases. The broader conclusion is that AI-driven CFD is not a single-model prescription: MLPs are effective for fast scalar responses, while POD--SINDy is better suited when transient reduced dynamics and field-derived statistics are central to the question.

physics.flu-dyn↗

arXiv2026

Characteristic Sensitivity Ensembles for Inference of Hidden Dynamics from Marginal Observations

A framework is developed for the inference of dynamics described by a generalized system of ordinary differential equations. A stochastic gradient method is coined that infers dynamics from observed marginal probability density functions using the joint probability density function of the observable and latent variables. Diffusion and other irreversible processes observed in a low-dimensional state can be recast as deterministic, reversible flows in a sufficiently augmented state space, where the joint density satisfies the hyperbolic Liouville equation. The marginal distribution observed is the projection of these hyperbolic dynamics onto the observed coordinates, with the latent components carrying the randomness and memory. This reframing allows inference for irreversible or stochastic dynamics into the recovery of a deterministic Ordinary Differential Equation (ODE) from marginal observations. Instead of solving the high-dimensional Liouville equation for the joint density, the algorithm exploits its characteristic representation. Particles sampled from the initial distribution are transported along characteristic lines. The Eulerian sensitivity with respect to parameters is obtained by sensitivity propagation along the characteristic lines, with a crossed U-statistic producing an unbiased gradient estimator, which enables stochastic gradient descent. Four experiments validate the method: recovery of a three-mode linear system observed through the marginal of a single mode; a nonlinear Gompertz growth model with a hidden mode; a bistable system whose hidden mode turns a unimodal marginal bimodal; and Stokes--Oseen drag law recovery for particles in a cellular flow. Convergence behavior is analyzed across these settings.

math.OC↗

arXiv2016

Regularization of singularities in the weighted summation of Dirac-delta functions for the spectral solution of hyperbolic conservation laws?

Singular source terms expressed as weighted summations of Dirac-delta functions are regularized through approximation theory with convolution operators. We consider the numerical solution of scalar and one-dimensional hyperbolic conservation laws with the singular source by spectral Chebyshev collocation methods. The regularization is obtained by convolution with a high-order compactly supported Dirac-delta approximation whose overall accuracy is controlled by the number of vanishing moments, degree of smoothness and length of the support (scaling parameter). An optimal scaling parameter that leads to a high-order accurate representation of the singular source at smooth parts and full convergence order away from the singularities in the spectral solution is derived. The accuracy of the regularization and the spectral solution is assessed by solving an advection and Burgers equation with smooth initial data. Nu- merical results illustrate the enhanced accuracy of the spectral method through the proposed regularization.

math.NA↗

arXiv2016

SPARSE: A Subgrid Particle Averaged Reynolds Stress Equivalent Model: Testing with A Priori Closure

A Lagrangian particle cloud model is proposed that accounts for the effects of Reynolds-averaged particle and turbulent stresses and the averaged carrier-phase velocity of the sub-particle-cloud scale on the averaged motion and velocity of the cloud. The SPARSE (Subgrid Particle Average Reynolds Stress Equivalent) model is based on a combination of a truncated Taylor expansion of a drag correction function and Reynolds averaging. It reduces the required number of computational parcels to trace a cloud of particles in Eulerian-Lagrangian methods for the simulation of particle-laden flow. Closure is performed in an a priori manner using a reference simulation where all particles in the cloud are traced individually with a point particle model. Comparison of a first-order model and SPARSE with the reference simulation in one-dimension shows that both the stress and the averaging of the carrier-phase velocity on the cloud subscale affect the averaged motion of the particle. A three-dimensional isotropic turbulence computation shows that only one computational parcel is sufficient to accurately trace a cloud of tens of thousand of particles.

physics.flu-dyn↗