Neural-network solution of subtracted three-body Faddeev integral equations near the Efimov limit

• URL: http://arxiv.org/abs/2606.10343v1
• Date: Tue, 09 Jun 2026 02:52:41 GMT
• Title: Neural-network solution of subtracted three-body Faddeev integral equations near the Efimov limit
• Abstract summary: Deep-neural-network (DNN) ansatz to the symmetrized spectator vector of the subtracted three-body Faddeev integral equation for identical bosons near the Efimov limit.<n>Network is trained by minimizing the residual of the discretized integral equation.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We apply a deep-neural-network (DNN) ansatz to the symmetrized spectator vector of the subtracted three-body Faddeev integral equation for identical bosons near the Efimov limit. The network is trained by minimizing the residual of the discretized integral equation, while the positive binding scale associated with the three-body energy is treated as a trainable parameter. Deterministic diagonalization of the same discretized kernel is used only as an a posteriori numerical benchmark. As preliminary validation, the neural-solver strategy is tested on the analytically solvable hydrogen radial problem. At unitarity, the DNN reproduces the Efimov ground-state binding scale with a DNN--deterministic deviation of $0.022\%$, while the first excited state is recovered to $0.002\%$. The deterministic solver recovers the universal Efimov scaling ratio $e^{2π/s_0}\simeq 515.03$, and the neural method traces the bound-state branches as a function of the inverse scattering length $1/a$ by continuation from the unitary solution. These results indicate that DNN-based residual minimization can provide a compact and differentiable representation of a renormalized few-body integral-equation solution in a regime governed by discrete scale invariance.

Related papers

• Circuit Depth Reduction of One-Ancilla Quantum Differential Equation Solver via Extrapolation [1.0742675209112622]
  A recent one-ancilla quantum differential equation solver provides a hardware-friendly and locality-preserving approach.<n>We reduce the maximum single-run circuit depth to $O(mathrmpolylog (1/)$ without adding quantum ancillae or sacrificing locality.<n> Numerical experiments on the Hatano-Nelson model (ODE) and the convection-diffusion equation (PDE) demonstrate the effectiveness of the approach.
  arXiv  Detail & Related papers  (2026-07-08T13:20:43Z)
• Physics-Informed Residuals for Adaptive Mesh Refinement in Finite-Difference PDE Solvers [0.0]
  This paper studies a hybrid strategy in which a physics-informed neural network (PINN) is used not as the final solver, but as an off-grid residual probe for adaptive mesh refinement.<n>The PINN residual is sampled over the domain, converted into cellwise indicators, and used to guide refinement before the final approximation is computed by a finite-difference solver.
  arXiv  Detail & Related papers  (2026-06-01T16:47:21Z)
• Hybrid Iterative Neural Low-Regularity Integrator for Nonlinear Dispersive Equations [0.0]
  HIN-LRI is a hybrid framework that augments a classical numerical solver with a neural operator trained to correct the solver's structured truncation error.<n>A lightweight neural network, operating on a low-dimensional latent manifold, learns the residual defect that analytical methods cannot close.<n>Experiments show that HIN-LRI improves accuracy over analytical, splitting methods, and neural PDE surrogates, with stable spatial refinement, effective out-of-distribution transfer, and modest online overhead.
  arXiv  Detail & Related papers  (2026-05-06T12:50:36Z)
• Learning with Norm Constrained, Over-parameterized, Two-layer Neural Networks [54.177130905659155]
  Recent studies show that a reproducing kernel Hilbert space (RKHS) is not a suitable space to model functions by neural networks. In this paper, we study a suitable function space for over- parameterized two-layer neural networks with bounded norms.
  arXiv  Detail & Related papers  (2024-04-29T15:04:07Z)
• A Mean-Field Analysis of Neural Stochastic Gradient Descent-Ascent for Functional Minimax Optimization [90.87444114491116]
  This paper studies minimax optimization problems defined over infinite-dimensional function classes of overparametricized two-layer neural networks. We address (i) the convergence of the gradient descent-ascent algorithm and (ii) the representation learning of the neural networks. Results show that the feature representation induced by the neural networks is allowed to deviate from the initial one by the magnitude of $O(alpha-1)$, measured in terms of the Wasserstein distance.
  arXiv  Detail & Related papers  (2024-04-18T16:46:08Z)
• Solving multiscale elliptic problems by sparse radial basis function neural networks [3.5297361401370044]
  We propose a sparse radial basis function neural network method to solve elliptic partial differential equations (PDEs) with multiscale coefficients. Inspired by the deep mixed residual method, we rewrite the second-order problem into a first-order system and employ multiple radial basis function neural networks (RBFNNs) to approximate unknown functions in the system. The accuracy and effectiveness of the proposed method are demonstrated through a collection of multiscale problems with scale separation, discontinuity and multiple scales from one to three dimensions.
  arXiv  Detail & Related papers  (2023-09-01T15:11:34Z)
• Physics-Informed Neural Network Method for Parabolic Differential Equations with Sharply Perturbed Initial Conditions [68.8204255655161]
  We develop a physics-informed neural network (PINN) model for parabolic problems with a sharply perturbed initial condition. Localized large gradients in the ADE solution make the (common in PINN) Latin hypercube sampling of the equation's residual highly inefficient. We propose criteria for weights in the loss function that produce a more accurate PINN solution than those obtained with the weights selected via other methods.
  arXiv  Detail & Related papers  (2022-08-18T05:00:24Z)
• Mean-field Analysis of Piecewise Linear Solutions for Wide ReLU Networks [83.58049517083138]
  We consider a two-layer ReLU network trained via gradient descent. We show that SGD is biased towards a simple solution. We also provide empirical evidence that knots at locations distinct from the data points might occur.
  arXiv  Detail & Related papers  (2021-11-03T15:14:20Z)
• Least-Squares ReLU Neural Network (LSNN) Method For Linear Advection-Reaction Equation [3.6525914200522656]
  This paper studies least-squares ReLU neural network method for solving the linear advection-reaction problem with discontinuous solution. The method is capable of approximating the discontinuous interface of the underlying problem automatically through the free hyper-planes of the ReLU neural network.
  arXiv  Detail & Related papers  (2021-05-25T03:13:15Z)
• Multipole Graph Neural Operator for Parametric Partial Differential Equations [57.90284928158383]
  One of the main challenges in using deep learning-based methods for simulating physical systems is formulating physics-based data. We propose a novel multi-level graph neural network framework that captures interaction at all ranges with only linear complexity. Experiments confirm our multi-graph network learns discretization-invariant solution operators to PDEs and can be evaluated in linear time.
  arXiv  Detail & Related papers  (2020-06-16T21:56:22Z)
• Neural Control Variates [71.42768823631918]
  We show that a set of neural networks can face the challenge of finding a good approximation of the integrand. We derive a theoretically optimal, variance-minimizing loss function, and propose an alternative, composite loss for stable online training in practice. Specifically, we show that the learned light-field approximation is of sufficient quality for high-order bounces, allowing us to omit the error correction and thereby dramatically reduce the noise at the cost of negligible visible bias.
  arXiv  Detail & Related papers  (2020-06-02T11:17:55Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.