This work introduces S-matrix informed neural networks (SINNs), and demonstrates their ability to learn scattering amplitudes directly from data while respecting first principles, and develops a novel data selection procedure which uses the response of constrained neural network ensembles to identify a set of experiments compatible with first principles.
Abstract
Reconstructing scattering amplitudes from finite, noisy, and mutually inconsistent measurements is an ill-posed inverse problem common to many reactions relevant to particle physics. We introduce S-matrix informed neural networks (SINNs), and demonstrate their ability to learn scattering amplitudes directly from data while respecting first principles. We further develop a novel data selection procedure, which uses the response of constrained neural network ensembles to identify a set of experiments compatible with first principles, and with each other. We apply this framework to $\pi\pi$ scattering, producing reusable amplitudes and correlated uncertainties without relying on a fixed functional form. We validate our results against residual model dependencies and training biases through closure tests and ablations. We find negligible impact of model architecture on our results. Our workflow unifies physics-constrained representation learning, data selection, and uncertainty quantification. Our strategy is transferable to other scattering processes, and other constrained physics problems limited by inconsistent data.
We present the first dispersive extraction of resonant poles from analytically continued neural networks. We use S-matrix informed neural networks (SINNs) trained to respect unitarity, analyticity, and crossing symmetry, without fixing a specific amplitude parametrization. The SINN framework controls representation dependence, enables constrained data selection, and enforces first principles. A large ensemble of networks trained on $\pi\pi$ scattering data propagates correlated uncertainties to all derived observables. We obtain robust determinations of the $\sigma/f_0(500)$, $\rho(770)$, and $f_0(980)$ poles of $\pi\pi$ scattering. Scattering lengths are determined alongside the amplitudes, while Adler zeroes emerge as predictions of the analytic structure. The results are stable against variations of the network architecture, and our approach can easily be adjusted for analysis of other reactions relevant to New Physics searches.
W. Smith, A. Rodas, Marius D. Thomas et al.· 0 citations
Electromagnetic inverse scattering is a nonlinear and ill-posed computational imaging problem, where accurate reconstruction is challenging due to measurement limitations, noise, and high computational costs, especially for 3-D imaging. Although physics-driven neural networks (PDNNs) reduce the dependence on labeled training data, existing accelerated PDNN frameworks often rely on preliminary reconstruction-based region selection, which may introduce instability when the selected region is inaccurate. In this paper, a coordinate-residual physics-driven neural network (CRPDNN) is proposed for 3-D electromagnetic inverse scattering. CRPDNN represents the unknown complex contrast distribution using normalized spatial coordinates and a residual convolutional network, whose parameters are optimized by enforcing consistency between the measured and model-predicted scattered fields. Unlike existing subregion-accelerated PDNN approaches, CRPDNN does not require a preliminary reconstruction, thereby avoiding dependence on its accuracy. For the reported noise-free 3-D synthetic cases, CRPDNN achieves an average relative error of 2.10\%, compared with 7.97\% for CSI and 3.99\% for $L_{2/3}$-FBE-WCIE, while providing approximately 5.5- and 12.1-fold speedups over the two baselines, respectively. Additional 2-D comparisons further demonstrate its stability and computational efficiency relative to existing PDNN frameworks. CRPDNN also maintains reliable reconstruction performance under noisy measurements, and the 3-D Fresnel experiments further indicate its potential for practical imaging applications.
Parameter identification in nonlinear dynamical systems is complicated by model-form uncertainty arising from systematic biases that violate the zero-mean error assumption of standard data assimilation methods. Recent neural-network-based approaches learn arbitrary bias corrections online. However, they require careful regularization to ensure unique solutions and carry computational overhead from ensemble propagation and in-situ training. We present a framework that integrates the parametrized-background data-weak formulation with attention-based parameter identification networks. It projects model error onto a dictionary of physically motivated spatial templates rather than learning arbitrary corrections. This provides uniqueness through hard subspace constraints rather than soft regularization penalties, albeit at the cost of restricting the representable bias space to patterns anticipated from domain knowledge. The framework is demonstrated on parameter estimation in the Rijke tube model, achieving robust generalization to out-of-distribution (OOD) bias patterns not seen during training. Ablation studies confirm the importance of state supervision for amplitude-sensitive parameters and temporal bias modeling for phase-sensitive parameters. Performance degrades gradually when bias patterns lie outside the template span. This indicates that the attention encoder extracts parameter information from bias-invariant features rather than relying critically on template-based bias capture. The physics-constrained and universal approximator approaches represent complementary points on the flexibility–efficiency tradeoff, suited to different operational contexts.
Y. Ju· Machine Learning: Science an...· 0 citations
Physics-Informed Neural Networks (PINNs) continue to suffer from limited training efficiency in predicting electromagnetic scattering from three-dimensional (3D) targets, resulting in particularly high retraining costs when target geometries or incident fields vary. To address this issue, we propose a transferable PINN framework constrained by discrete Maxwell operators. By embedding finite-difference electromagnetic operators into the loss function, the predicted fields directly satisfy the discrete Maxwell’s equations on the computational grid, thereby enhancing physical consistency and improving training stability. Furthermore, a layer-freezing strategy is employed to preserve the generalized wave priors learned from the source scenario. Consequently, training under novel geometries or incident conditions no longer relies on full-network retraining; instead, rapid prediction is achieved by fine-tuning a minimal set of task-specific parameters. Numerical results demonstrate that the proposed method significantly reduces the number of iterations and retraining costs while maintaining prediction accuracy, making it an effective tool for rapid electromagnetic simulations and optical device design.
The results demonstrate that PINN achieves more accurate and stable full-field vibration reconstructions than conventional PINNs, particularly under conditions involving high-frequency modes, and highlights the potential of hybrid data-physics neural frameworks as an efficient and reliable approach for solving complex PDE-governed dynamical systems.
Hai-Long Liu, S. Hedayatrasa, Yunpeng Zhu et al.· e-Journal of Nondestructive...· 0 citations
Transport-dominated problems remain challenging for data-driven methods, which often exhibit severe numerical oscillations near shocks or steep gradients due to globally supported basis functions or overly smooth hypothesis spaces. Gegenbauer reconstruction has shown promise in mitigating such oscillations, but its effectiveness critically depends on the reconstruction parameters, particularly the weight parameter $\lambda$ and truncation order $m$. For data-driven models, variations in governing problems, training data, and model architectures make systematic parameter selection particularly challenging. To address this issue, we propose a physics-informed machine-learning framework that predicts probability distributions over candidate Gegenbauer parameter pairs, enabling probabilistically weighted reconstruction while accounting for parameter uncertainty. A two-stage strategy is adopted, in which a general predictor is first pre-trained and then fine-tuned for target problems to balance accuracy and computational cost. The framework is evaluated for reduced-order and neural operator models, represented by POD-Galerkin and DeepONet, respectively. Numerical experiments on one- and two-dimensional transport-dominated problems show that the framework learns effective spatially adaptive parameter distributions. Compared with conventional reconstruction strategies, it reduces numerical errors by up to one to two orders of magnitude and achieves a more favorable accuracy--cost trade-off than problem-specific model retraining.
Lei Yan, Yan Jiang· 0 citations
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