Fast & accurate emulation of two-body scattering observables without wave functions

Model reduction methods for nuclear emulators

“…Furthermore, a new approach for emulating directly scattering K or T matrices (without trial wave functions) was proposed in Ref. [24] based on the Newton variational principle (NVP) [58]. Each of these methods has benefited from an affine parameterization of the Hamiltonian H(θ), which permitted fast & accurate emulation of nuclear observables.…”

“…Indeed, the nuclear physics community has recently been exploiting an already-established modeldriven, projection-based PMOR technique in the study of the eigenvalue problem. Introduced to the nuclear community as eigenvector continuation (EC) [19,20], this method has been demonstrated to be highly effective for nuclear bound-state [3,5,21,22] and scattering calculations [23][24][25][26]. EC has not been recognized in its broader context because the projection techniques common in the model reduction literature are not widely known in the nuclear physics community.…”

Fast emulation of quantum three-body scattering

“…In short, the eigenvectors from the training solutions can be used as an extremely effective basis for variational estimates. In nuclear physics, fast and accurate EC emulators have been developed recently for few-and many-body ground states [10][11][12], excited states [13], and transitions [12]; for shell-model calculations [14]; and, of particular relevance here, for two-body scattering [15][16][17]. They are particularly efficacious for Bayesian statistical analyses, where extensive sampling in the parameter space is typically needed for parameter estimation, propagation of errors to observables, and experimental design.…”

“…It should be emphasized that the Ψ are not limited to wave functions, but can be general objects that are variates for the functionals. In Ref [16],. the object is the scattering K-matrix.…”

Self-learning Emulators and Eigenvector Continuation

“…This projection reduces the computational complexity greatly, and EC allows one to compute the eigenvector in a region of the parameter where it was not computationally feasible to solve the eigenvalue problem directly and has been used for dealing with Monte Carlo sign oscillations [12] and as a resummation method for perturbation theory [13,14]. Recently it was observed that EC can function as an accurate emulator for quantum systems [8], and this was followed by a number of new developments and applications [9,[15][16][17][18][19][20]. The implementation of EC within an active learning framework was first discussed in [21].…”