APRIL: Auxiliary Physically-Redundant Information in Loss -- A physics-informed framework for parameter estimation with a gravitational-wave case study

Abstract

Physics-Informed Neural Networks (PINNs) embed the partial differential equations (PDEs) governing the system under study directly into the training of Neural Networks, ensuring solutions that respect physical laws. While effective for single-system problems, standard PINNs scale poorly to datasets containing many realizations of the same underlying physics with varying parameters. To address this limitation, we present a complementary approach by including auxiliary physically-redundant information in loss (APRIL), i.e. augment the standard supervised output-target loss with auxiliary terms which exploit exact physical redundancy relations among outputs. We mathematically demonstrate that these terms preserve the true physical minimum while reshaping the loss landscape, improving convergence toward physically consistent solutions. As a proof-of-concept, we benchmark APRIL on a fully-connected neural network for gravitational wave (GW) parameter estimation (PE). We use simulated, noise-free compact binary coalescence (CBC) signals, focusing on inspiral-frequency waveforms to recover the chirp mass $\mathcal{M}$, the total mass $M_{\mathrm{tot}}$, and symmetric mass ratio $\eta$ of the binary. In this controlled setting, we show that APRIL achieves up to an order-of-magnitude improvement in test accuracy, especially for parameters that are otherwise difficult to learn. This method provides physically consistent learning for large multi-system datasets and is well suited for future GW analyses involving realistic noise and broader parameter ranges.

References in corpus (18)

• Advanced Virgo: a 2nd generation interferometric gravitational wave detector
• Advanced LIGO
• DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators
• Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries
• Enhancing Gravitational-Wave Science with Machine Learning
• The basic physics of the binary black hole merger GW150914
• Solving the Teukolsky equation with physics-informed neural networks
• Applications of machine learning in gravitational wave research with current interferometric detectors
• Status of GEO 600
• Magnetohydrodynamics with Physics Informed Neural Operators
• Modelling Force-Free Neutron Star Magnetospheres using Physics-Informed Neural Networks
• Using physics-informed neural networks to compute quasinormal modes
• Machine Learning for Conservative-to-Primitive in Relativistic Hydrodynamics
• Learning orbital dynamics of binary black hole systems from gravitational wave measurements
• Solving the Pulsar Equation using Physics-Informed Neural Networks
• GWTC-4.0: Population Properties of Merging Compact Binaries
• Explainable autoencoder for neutron star dense matter parameter estimation
• Adaptive Physics-informed Neural Networks: A Survey