Reduced basis emulator for elastic scattering in continuum-discretized coupled-channel calculations

TL;DR

This work tackles the computational bottleneck of continuum-discretized coupled-channel (CDCC) calculations under uncertain optical potentials by introducing a POD-based reduced basis emulator. Training on full CDCC solutions at Latin hypercube-sampled parameters, the method constructs per-$J$ reduced bases and predicts new solutions via Galerkin projection, achieving about $10^2$× speedups with sub-percent accuracy. Validation on deuteron+$^{58}$Ni scattering at $E_{ ext{lab}}=21.6$ MeV shows accurate reproduction of elastic cross sections across 18 parameters, with detailed tests on $S_{11}^J$, wavefunction coefficients, and angular distributions. This emulator enables practical uncertainty quantification and Bayesian parameter estimation for CDCC, paving the way for systematic studies, including halo nuclei and energy-systematics, at feasible computational costs.

Abstract

I develop a reduced basis emulator for continuum-discretized coupled-channel (CDCC) calculations that achieves speedups of $\sim 10^2$ while maintaining sub-percent accuracy. The emulator is constructed using the proper orthogonal decomposition (POD) method applied to snapshots of CDCC solutions computed at sampled points in the optical potential parameter space. The prediction is performed via Galerkin projection onto the reduced basis. I demonstrate the method using deuteron scattering on $^{58}$Ni at 21.6 MeV as a test case, emulating 18 optical potential parameters simultaneously. The emulator reproduces elastic scattering cross sections with errors below 0.1\% across a wide parameter range. This development enables efficient uncertainty quantification and Bayesian parameter estimation for nuclear reaction calculations that were previously computationally prohibitive.

Figures (7)

• Figure 1: Schematic of the reduced basis emulator workflow. The offline stage (left, blue) generates snapshots by solving the full CDCC problem at $N_s$ sampled parameter values, constructs a joint snapshot matrix for all channels, extracts the reduced basis via SVD truncation, and precomputes parameter-independent matrices. The online stage (right, green) rapidly evaluates new parameter points by building the potential matrix, performing Galerkin projection onto the reduced basis, solving the small $n_b \times n_b$ linear system, and reconstructing the full solution to obtain the differential cross section $d\sigma/d\Omega$.
• Figure 2: Partial-wave elastic cross sections $\sigma_J$ versus total angular momentum $J$ for five test parameter sets. Black solid lines: exact CDCC calculations. Blue dashed lines with triangles: emulator predictions with $N_{\text{sample}} = 200$. Red dotted lines with squares: emulator predictions with $N_{\text{sample}} = 400$. The three curves overlap almost perfectly.
• Figure 3: Elastic $S$-matrix element $S_{11}^J$ for Test 1 with the emulator trained using $N_s = 200$ samples. (a) Real part. (b) Imaginary part. Black circles with solid lines: exact CDCC calculation. Red squares with dashed lines: emulator prediction.
• Figure 4: Relative error in the magnitude of the elastic $S$-matrix element $|S_{11}^J|$ versus $J$ for five test cases. Blue solid lines with triangles: $N_{\text{sample}} = 200$. Red dashed lines with squares: $N_{\text{sample}} = 400$.
• Figure 5: Elastic channel wave function coefficient $c_1(r)$ for $J = 0$ (Test 1) with the emulator trained using $N_s = 200$ samples. (a) Real part. (b) Imaginary part. Black solid lines: exact CDCC calculation. Red dashed lines: emulator prediction.