# On the joint estimation of flow fields and particle properties from Lagrangian data

arXiv: https://arxiv.org/abs/2510.00479 · HTML: https://mlsanity.com/paper/2510.00479/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 139 references that are in the map.
- First posted on arXiv 1 Oct 2025.

## Builds on (most cited first, 8 of 8)

- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [PirateNets: Physics-informed Deep Learning with Residual Adaptive Networks](https://mlsanity.com/paper/2402.00326/) (2024)
- [Gradient Alignment in Physics-informed Neural Networks: A Second-Order Optimization Perspective](https://mlsanity.com/paper/2502.00604/) (2025)
- [Multi-stage Neural Networks: Function Approximator of Machine Precision](https://mlsanity.com/paper/2307.08934/) (2023)
- [Machine Learning Holography for 3D Particle Field Imaging](https://mlsanity.com/paper/1911.00805/) (2019)
- [Regularized Inverse Holographic Volume Reconstruction for 3D Particle Tracking](https://mlsanity.com/paper/1904.04884/) (2019)
- [Volumetric Particle Tracking Velocimetry (PTV) Uncertainty Quantification](https://mlsanity.com/paper/1911.12495/) (2019)

## Abstract (arXiv)

We numerically investigate the feasibility and limits of jointly estimating flow fields and unknown particle properties (e.g., position, size, and density) from Lagrangian particle tracking (LPT) data. LPT offers time-resolved, volumetric measurements of particle trajectories, which are markers of the carrier fluid motion. However, experimental tracks are spatially sparse and potentially noisy, and the problem of reconstructing flow fields may be further complicated by inertial particle transport, such that particle slip velocities must be determined to access the velocity field of the carrier fluid. To address this problem, we develop a data assimilation framework that couples an Eulerian representation of the flow with Lagrangian particle models, enabling the simultaneous inference of carrier fields and particle properties under the governing equations of disperse multiphase flow. We show that flow fields and particle properties can be jointly estimated in three representative regimes: (1) In a turbulent boundary layer with noisy tracer tracks (St to 0), flow fields and true particle positions are jointly estimated, which amounts to a physics-informed particle tracking problem; (2) in homogeneous isotropic turbulence seeded with inertial particles (St ~ 1-5), we demonstrate simultaneous recovery of flow states and particle diameters, showing the feasibility of implicit particle characterization; and (3) in a compressible, shock-dominated flow, we report the first joint reconstructions of velocity, pressure, density, and inertial particle properties (diameter and density), highlighting both the potential and certain limits of joint estimation in supersonic regimes. A systematic sensitivity study reveals how the seeding density, noise level, and Stokes number govern reconstruction accuracy for our method.