Solving two and three-body systems with deep neural networks

Abstract We develop a method for solving two- and three-body bound state problems using unsupervised machine learning with deep neural networks (DNN). By taking coordinates as direct inputs, the DNN provides a functional-ansatz-free alternative to traditional methods, allowing for a vast exploration of the parametric space. We apply this technique to calculate the properties of the deuteron and triton using a realistic chiral effective field theory ( $$\chi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>χ</mml:mi> </mml:math> EFT) potential at N $$^3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>3</mml:mn> </mml:mmultiscripts> </mml:math> LO, explicitly including central, tensor, and spin-orbit forces. Our results demonstrate high precision in binding energies and wave function structures. This approach offers a promising framework for the study of nuclear and hadronic many-body problems.