Neural quantum networks and the quantum states (NQS) they represent have been shown to deliver exceptional performance as surrogate models for problems in many-body quantum systems. Traditionally, NQS lack interpretability because of the distributed, network-wide encoding of the quantum state.

To increase interpretability of NQS, this work extends Kolmogorov-Arnold Networks (KANs) to ground state and electronic wavefunction prediction.^[1] The output of the wavefunction, Psi-KAN (PKAN), is the minimized ground state energy and 1-d functions composable into a full wavefunction. KANs are predicated on learning flexible functions between network nodes, which increases interpretability by extracting the individual functions along with decreasing the network size by efficient composition of functions for NQS fitting.

PKANs scale in width as O(n³), where n is the number of electrons, while the network's depth is restricted to two hidden layers. The separability of wavefunctions into radial and angular functions is taken into account as KANs learn 1-d that are composable by addition and multiplication.

Fig. 1: Representation of a two electron PKAN model with learned separable 1-d functions for each electron.

In testing PKAN models on single electron wavefunctions of hydrogen, the model learns the correct radial and angular nodal structure. Of note is that the overall sign of the wavefunction is correct but individual functions are of the opposite sign. Enforcing sign constraints by a physics-informed loss function should resolve the sign issue.

Looking forward a Born-Oppenheimer approximation loss function and a local gradient calculation of the loss function will be implemented by variational Monte Carlo.^[2] The hope is to make PKAN an ab-initio method. Additionally, including explicit multi-electron interactions within the network is underway.

[1] KAN: Kolmogorov–Arnold Networks
[2] A Self-Attention Ansatz for Ab-initio Quantum Chemistry