arXiv subjects

Nicolas Tricard

Publications and source records attributed to Nicolas Tricard.

4 recordsLinked to original sources

arXiv2026

FlowReconBench: Accuracy, calibration and cost of learned and classical flow reconstruction from sparse sensors

Reconstructing full flow fields from sparse sensors requires prior assumptions about unmeasured regions and physical variables. Yet it remains unclear when learned models outperform classical estimators and which aspects of their predictions can be trusted. FlowReconBench evaluates ten learned and five classical methods on three regimes: a laminar cylinder wake across Reynolds numbers, two-dimensional Kolmogorov turbulence and a large-scale three-dimensional (3D) isotropic turbulence. Methods share leakage-controlled splits and sensor draws and are scored on per-channel error, ensemble spread, calibration, spectra and cost. The leading method changes for each regime. Classical methods perform strongly in low-order and dense-sensing regimes. On the cylinder wake, linear stochastic estimation and gappy proper orthogonal decomposition lead, including for unobserved pressure. In 3D, inverse-distance weighting matches the best learned methods on observed channels. Data-driven methods become superior at decreasing sensor density or poor sensor observability. On Kolmogorov flow, continuous ranked probability score and error yield different method rankings: generative models offer broader but underdispersed ensembles, while deterministic models prioritize pointwise error. Generative models balance this tradeoff through their sampler budget, with a larger budget improving ensemble quality at higher computational cost. In 3D, scaling tests demonstrate that queryable methods are flat in memory, while full-grid construction methods run out of memory. Observing only 2 of 4 fields leaves the problem kinematically underconstrained, yet a latent model can reproduce structural similarities to the ground truth.

physics.flu-dyn↗

arXiv2026

Sparse Reconstruction by Direct Measurement-to-Field Generation in Function Space

Understanding physical systems often requires recovering their full spatial state from measurements available only at sparse locations. This reconstruction becomes challenging when physical boundaries are unknown, high-resolution training fields are unavailable, or important quantities cannot be measured directly. Sparse observations may also be consistent with multiple plausible states, leading to significant reconstruction uncertainty. Here we introduce Direct Measurement-to-Field Generation (\DMF{}), a functional rectified flow framework that learns how sparse measurements drive physical-field generation end to end. Instead of relying on grid-based rasterization or runtime guidance, \DMF{} jointly learns a sensor--global--sensor representation with the generative transport, dynamically fusing local grounding with global context to evaluate physical fields at arbitrary query coordinates. Across benchmarks involving unobserved boundaries, missing high-resolution training fields, and unmeasured physical quantities, \DMF{} outperforms alternative baselines by significantly reducing reconstruction errors and preserving the fidelity of physical properties. Furthermore, its stochastic ensemble generation reliably quantifies uncertainty while improving continuous ranked probability scores. These results extend sparse reconstruction from fixed-setting point estimation toward measurement-conditioned generation of physical fields under incomplete and changing information.

cs.LG↗

arXiv2026

3-D Representations for Hyperspectral Flame Tomography

Flame tomography is a compelling approach for extracting large amounts of data from experiments via 3-D thermochemical reconstruction. Recent efforts employing neural-network flame representations have suggested improved reconstruction quality compared with classical tomography approaches, but a rigorous quantitative comparison with the same algorithm using a voxel-grid representation has not been conducted. Here, we compare a classical voxel-grid representation with varying regularizers to a continuous neural representation for tomographic reconstruction of a simulated pool fire. The representations are constructed to give temperature and composition as a function of location, and a subsequent ray-tracing step is used to solve the radiative transfer equation to determine the spectral intensity incident on hyperspectral infrared cameras, which is then convolved with an instrument lineshape function. We demonstrate that the voxel-grid approach with a total-variation regularizer reproduces the ground-truth synthetic flame with the highest accuracy for reduced memory intensity and runtime. Future work will explore more representations and under experimental configurations.

cs.CV↗

arXiv2026

GLU: Global-Local-Uncertainty Fusion for Scalable Spatiotemporal Reconstruction and Forecasting

Digital twins of complex physical systems are expected to infer unobserved states from sparse measurements and predict their evolution in time, yet these two functions are typically treated as separate tasks. Here we present GLU, a Global-Local-Uncertainty framework that formulates sparse reconstruction and dynamic forecasting as a unified state-representation problem and introduces a structured latent assembly to both tasks. The central idea is to build a structured latent state that combines a global summary of system-level organization, local tokens anchored to available measurements, and an uncertainty-driven importance field that weights observations according to the physical informativeness. For reconstruction, GLU uses importance-aware adaptive neighborhood selection to retrieve locally relevant information while preserving global consistency and allowing flexible query resolution on arbitrary geometries. Across a suite of challenging benchmarks, GLU consistently improves reconstruction fidelity over reduced-order, convolutional, neural operator, and attention-based baselines, better preserving multi-scale structures. For forecasting, a hierarchical Leader-Follower Dynamics module evolves the latent state with substantially reduced memory growth, maintains stable rollout behavior and delays error accumulation in nonlinear dynamics. On a realistic turbulent combustion dataset, it further preserves not only sharp fronts and broadband structures in multiple physical fields, but also their cross-channel thermo-chemical couplings. Scalability tests show that these gains are achieved with substantially lower memory growth than comparable attention-based baselines. Together, these results establish GLU as a flexible and computationally practical paradigm for sparse digital twins.

cs.LG↗