Addressing the ground state of the deuteron by physics-informed neural networks

summary

The gist

The gist The PINN framework allows for addressing realistic nucleon-nucleon interactions in momentum space to obtain highly accurate results for the deuteron ground state, demonstrating feasibility

In short

Researchers used Physics-Informed Neural Networks (PINNs) to find the ground state of a deuteron by solving its many-body Schrödinger problem using realistic nucleon-nucleon interactions in momentum space. The method achieved highly accurate results, with a relative error of $10^{-6}$ compared to numerical benchmarks, proving PINNs are feasible for complex nuclear structure problems.

Key concepts

Physics-Informed Neural Networks (PINNs): PINNs are a machine learning technique that solves differential equations by incorporating the governing physical laws directly into the network's loss function. This allows the neural network to learn solutions to complex problems, like the Schrödinger equation, without needing extensive training data or explicit prior knowledge of all physical constraints.
Loss Function Components (LPINN): The overall loss function for PINNs is a combination of several terms: LPDE (for solving the differential equation), Ldata (for supervised learning), LBCs (for boundary conditions in coordinate space), Lnorm (to enforce normalization), and Lvar (to implement the variational principle). This comprehensive loss function ensures the network learns a physically consistent wavefunction.
Momentum Space Simulations: The study tested two realistic nucleon-nucleon interaction models in momentum space: N4LO, which uses a cutoff of 550 MeV/c, and CD-Bonn, which extends up to several GeV/c. These simulations showed that the accuracy of the results is largely dictated by the potential model itself rather than the PINN method.
Variational Energy Loss (Lvar): The variational principle is implemented in the loss function through Lvar. This term forces the network's predicted wavefunction to adhere to physical constraints derived from minimizing energy, ensuring that the resulting solution behaves qualitatively like a bound L=0 wave, concentrating probability where the nuclear interaction is most attractive.

Terminology used across episodes

Reinforcement Learning (RL) — explained in 25 episodes
Sample Complexity — explained in 18 episodes
Federated Learning — explained in 17 episodes
Retrieval-Augmented Generation (RAG) — explained in 16 episodes
Interpretability — explained in 15 episodes
Quantum Fisher Information (QFI) — explained in 15 episodes

This episode discusses

The paper

Addressing the ground state of the deuteron by physics-informed neural networks · Read on arXiv

Dipartimento di Fisica "Aldo Pontremoli" UniversitaÓ di Milano International Centre for Theory of Quantum Technologies University of Gdansk INFN Seziona di Milano

DOI: 10.1016/j.physletb.2026.141050

Transcript

Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "Addressing the ground state of the deuteron by physics-informed neural networks".

Mira: The gist The PINN framework allows for addressing realistic nucleon-nucleon interactions in momentum space to obtain highly accurate results for the deuteron ground state,

Kai: First, who's behind it and why it matters.

Paper summary: Kai: So we've covered how this paper, "Addressing the ground state of the deuteron by physics-informed neural networks," uses PINNs to tackle realistic nucleon-nucleon interactions in momentum space to get highly accurate results for the deuteron ground state.

Mira: The authors are essentially showing that they can solve a manybody Schrödinger problem using this framework, introducing a new strategy for computing eigenenergies that extends the standard PINN approach. They provide examples of analogous simulations in coordinate space as well.

Lev: From what I see, the main thing this paper does is prove that PINNs can be applied to an ab initio nuclear structure problem, which is a big step because it's not just solving some simple toy model.

Kai: The authors conclude that their approach paves the way for exploiting PINNs to solve more complex atomic nuclei in the future, even though they only showed the deuteron here.

Mira: It suggests that this method of integrating all possible physical knowledge into a loss function is a viable path forward when dealing with complex quantum systems where you might lack target data.

Lev: The limitation they state is that their implementation doesn't extend to full three dimensional space yet, so we know exactly what the next engineering hurdle looks like for taking this from the deuteron to something more substantial.

Conclusion: Kai: So, we've seen how they took realistic nucleon-nucleon interactions in momentum space and used physics to train a neural network to get highly accurate results for the deuteron ground state.

Mira: It’s a specific problem, solving that manybody Schrödinger equation using these PINNs, which is really pushing what you can do with these architectures.

Lev: From my side, I'm thinking about how much overhead that training process adds when we try to run this kind of calculation on actual quantum hardware.

Kai: Yeah, it’s a demonstration of feasibility, showing the method works for this simple system before we try something more complex.

Mira: It means these physics-informed networks aren't just theoretical exercises; they have the potential for ab initio nuclear structure problems.

Lev: But you gotta remember, this was done in momentum space simulations with specific interactions like N4LO and CD-Bonn, not necessarily the full three dimensions we want to aim for yet.

Kai: That’s right; they showed excellent agreement with numerical benchmarks, with a relative error down to about ten-six.

Mira: That level of precision is what makes this approach so compelling for solving these complex quantum systems.

Lev: And it sets a benchmark for how we can use machine learning to find those bound states in nuclear physics.

Kai: It opens the door, then, to using PINNs as a tool instead of just a black box when dealing with the manybody problem.

Mira: Exactly; integrating the variational principle directly into the loss function is that crucial physical constraint they're exploiting.

Lev: It shows that we can start leveraging these tools for nuclear structure right now, even if it’s just for testing concepts like this deuteron example.

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