Understanding Heavy-ion Fusion Cross Section Data Using Novel Artificial Intelligence Approaches

An unprecedentedly extensive dataset of complete fusion cross section data is modeled via a novel artificial intelligence approach. The analysis was focused on light-to-medium-mass nuclei, where fission-like phenomena are more difficult to occur. The method used to derive the models exploits a state-of-the-art hybridization of genetic programming and artificial neural networks and is capable to derive, in a data-driven way, an analytical expression that serves to predict integrated cross section values. We analyzed a comprehensive set of nuclear variables, including quantities related to the nuclear structure of projectile and target. In this paper, we describe the derivation of two computationally simple models that can satisfactorily describe, with a reduced number of variables and only a few parameters, a large variety of light-to-intermediate-mass collision systems in an energy domain ranging approximately from the Coulomb barrier to the oncet of multi-fragmentation phenomena. The underlying methods are of potential use for a broad domain of applications in the nuclear field.

• Different, complementary, experimental methods can be effectively used to estimate the yield of evaporation residues (gamma-ray analysis, time-of-flight and magnetic spectrometers, charged particle detection with telescope arrays) → heavy-ion fusion cross section from the Coulomb barrier to the onset of multi-fragmentation → • See e.g.P. Frobrich, Phys. Rep. 116 (1984) 337.
S. Pirrone et al., Eur.J. Phys.J.A. (2019) 55: 22 → higher probability of fusion-evaporation and fission-like processes for higher N/Z content in entrance channel.
F. Amorini et al., Phys. Rev. Lett. (2009) 102: 112701 → Isospin effects on the competition between fusion-like processes and binary-like mechanisms.→ Larger probability to produce heavy-residue for the systems with the largest neutron content.→ Sensitivity to the density dependence of the symmetry energy term of the nuclear EoS using microscopic approaches.
→ Also recent results by INDRA-FAZIA support these findings!

Complete fusion reactions: a brief overview
Models for the description of fusion cross section between heavy-ions: • Microscopical approaches: Time-Dependent Hartree Fock (TDHF), Molecular dynamics; • Macroscopic models: critical distance models, limitation to the compound nucleus model (empirical nuclear potentials from semi-classical considerations); • Empirical models: starting from nuclear reaction theory and then optimizing to the experimental data.

Complete fusion reactions: a brief overview
More recently → systematic study of Region III shows discrepancies for some of the systems → further investigation on both experiment and theory is required!Fusion cross section in Region III → disagreement with the prediction of state-of-the-art for some collision systems such as:

Approach, dataset, and modeling
Approach: supervised learning using symbolic regression algorithms.

Novelties:
• Deriving mathematical expressions to describe the data → support to theories and models attempting to predict the fusion cross section between heavy-ions; • Comprehensive analysis of large amount of nuclear data → universal model for the description of the entire dataset; • Advanced feature selection → allows to inspect the dependence on several variables (including nuclear structure variables).

Major challenges:
• The amplitude of the cross section varies even by several orders of magnitude with the energy; • Experimental errors associated to each individual data point differ by several orders of magnitude for each data point; • Resulting models must have physical boundaries and extrapolation capabilities.
We used an extensive set of nuclear features linked to: 1) The nature of the collision partners; 2) The energy of the collision; 3) The structure of the collision partners; 4) The structure of the compound nucleus.
• Dataset used for model derivation → about 4500 experimental data points.

The Brain Project
Brain Project -a neural-genetic tool for the formal modeling of data The Brain Project: genetic mechanism  • One of the key aspects of these methods is the advanced feature selection, implemented via a programming simulation of the natural selection → help to probe the existence of correlations between variables; • The present application focused on modeling an unprecedently large dataset of heavy-ion fusion cross section data and a broad body of nuclear variables; • The newly developed models are capable to describe the entire systematics with a few variables, which are found to contain the whole informative content of a larger set of variables; • These methods are readily applicable to numerous datasets in the nuclear domain!
Thank you for your attention!
Exploits a novel hybridization of genetic programming and artificial neural network → the task is that of symbolic regression.Genetic part → foresees the evolution of tree-like structures representing mathematical expressions → deals with the global search for the maximum of a suitable fitness function; Neural part → deals with the local search for the minimum of the error when the genetic part has identified a good maximum of the fitness function.Genetic evolution of tree-like structures representing mathematical expressions + Artificial neural networks to optimize the constants (gradient descent technique)

Fitness
function → is the function to maximize → it suitably contains the prediction error and a term related to the complexity of the model and/or feature costs.13/06/2023 -Varenna (Italy) Daniele Dell'Aquila (daniele.dellaquila@unina.it) 15 to tune the desired trade-off between accuracy and complexity related to the accuracy of the model related to the complexity of the model Results   =   ⋅    −   → required to reach a predefined, target, number of nodes.Brain Project usually tries to optimize the error with a given number of nodes → interesting to more easily tune the complexity of the desired model.Comparison with other models 13/06/2023 -Varenna (Italy) → The feature selection can help to inspect shell effects in the reaction cross sections… Difficult with traditional analysis methods! • Artificial Intelligence approaches based on hybridization of genetic programming and artificial neural networks are promising to help the description and understanding of large datasets of nuclear variables;