Physics-Informed Machine Learning for Acoustic Holography / Holographie acoustique basée sur l’[...]

Overview

PhD offer (starting date: Fall 2026).

Context and Objectives

Near-field acoustic holography is an imaging technique based on the measurement of the acoustic field using a microphone array. It enables the reconstruction of acoustic quantities (pressure, particle velocity, intensity) in the vicinity of sound sources, providing a precise spatial and frequency-domain representation of acoustic radiation. Introduced by Williams (1), acoustic holography has gained widespread adoption due to its many advantages: no assumptions on the nature of the sources, sub-half-wavelength spatial resolution, access to multiple field components, and adaptability to both stationary and non-stationary configurations (2). Reconstructing the acoustic field from near-field measurements constitutes an inverse problem, which has been extensively studied using various regularization strategies, including Tikhonov regularization (3), Bayesian approaches (4), and compressive sensing or sparse regularization methods (5).

However, with the emergence of Physics-Informed Neural Networks (PINNs), new approaches can now be considered to address the inverse problem of acoustic field reconstruction (6). Recent studies have begun to explore this research direction (7–12). For instance, the authors of (7) proposed a method to estimate and reconstruct the sound field of a room from a limited set of experimental impulse responses using a PINN framework. Acoustic wave propagation has also been investigated using PINNs in (8), including scenarios involving obstacles of various shapes and sizes (9). Furthermore, the Kirchhoff–Helmholtz integral has been employed to incorporate physical constraints into the forward simulation of acoustically reconstructed fields (10, 11). This principle was extended by Luan et al. (12), who proposed a hybrid approach combining PINNs with sparse field discretization for planar acoustic holography.

These advances position PINNs as strong candidates to overcome several long-standing limitations of acoustic holography:

• Continuous field reconstruction without restriction to a discrete mesh;
• Reconstruction from potentially irregular measurement configurations;
• Solution of the inverse problem with reduced computational complexity;
• Extrapolation of the reconstructed field beyond the measurement region.

In addition to PINNs, recent approaches based on Fourier Neural Operators (FNOs) offer a powerful and highly generalizable alternative (13). FNOs aim to solve inverse problems by learning operators through collocation in Fourier space.

Objectives

1. Explore and formalize the use of PINNs for acoustic holography: investigate the application of PINNs for acoustic field reconstruction, focusing on planar holography using planar microphone arrays, with the aim of modeling the acoustic field by directly embedding the governing physical equations into the learning process. This PINN-based formulation constitutes the core originality of the work and will enable an assessment of their potential to surpass the limitations of conventional approaches.
2. Experimentation and validation on real-world cases: perform experimental validation on realistic configurations. Measurements will be conducted using the laboratory’s microphone arrays and data acquisition systems, complemented by simulations of known acoustic fields (e.g., radiation from a vibrating plate). Compare PINN-based models with classical acoustic holography techniques (Tikhonov, compressive, Bayesian) in terms of accuracy, robustness, and computational complexity.
3. Extension to non-stationary acoustic fields: start with stationary fields and extend to time-varying situations. Develop a time-dependent formulation for non-stationary sources and investigate the feasibility of real-time acoustic holography.
4. Development and evaluation of an FNO-based approach: explore using FNOs to learn the inverse operator mapping near-field measurements to source-level acoustic fields, and evaluate on simulated and experimental datasets, comparing with PINN-based results.

Such a PhD project would contribute to the development of an innovative diagnostic tool for systems whose emitted sounds vary according to their operational state and would foster expertise within the laboratory in physics-informed learning.

Profile

We are looking for a student enrolled in a master’s degree in acoustics or related fields, with an interest in acoustic imaging, artificial intelligence and signal processing. They will develop skills in both modeling and experimentation.

Location and Environment

The student will conduct their research at the Laboratory of Acoustics of Le Mans University (LAUM, Le Mans, France), which specializes in acoustics.

Contacts

• Jean-Hugh Thomas (jean-hugh.thomas at univ-lemans.fr)

Funding category: Contrat doctoral

Endowment of a French institution with a research mission

PHD Country: France