用神经网络破解暗物质生成机制，仅凭一个观测数据反推宇宙演化与粒子性质
Unraveling particle dark matter with Physics-Informed Neural Networks
- 用物理信息神经网络求解暗物质冻结产生方程，无需网格离散化
- 仅用宇宙暗物质密度观测值，就确定了宇宙膨胀指数和粒子相互作用截面
- 揭示了宇宙膨胀快慢与粒子作用强弱的对应关系，适合暗物质与宇宙学交叉研究者
我们采用无网格的物理信息神经网络（PINNs）方法，参数化求解在另类宇宙学模型中冻结产生暗物质（DM）所遵循的玻尔兹曼方程。通过逆向PINNs，仅利用一个实验观测点——暗物质残留密度，便推断出理论中的物理属性，包括受膜世界模型启发的幂律宇宙学参数以及粒子相互作用截面。此类另类宇宙学中宇宙膨胀被参数化为一个类似开关的函数，可重现后期哈勃定律；我们更以平滑函数实现更真实的过渡建模。研究发现：对于负（正）幂律指数的宇宙学，需较小（较大）的相互作用截面才能匹配观测数据。最后，通过贝叶斯方法量化了逆问题中理论参数的认知不确定性。
原文摘要 · Abstract (English)
We parametrically solve the Boltzmann equations governing freeze-in dark matter (DM) in alternative cosmologies with Physics-Informed Neural Networks (PINNs), a mesh-free method. Through inverse PINNs, using a single DM experimental point -- observed relic density -- we determine the physical attributes of the theory, namely power-law cosmologies, inspired by braneworld scenarios, and particle interaction cross sections. The expansion of the Universe in such alternative cosmologies has been parameterized through a switch-like function reproducing the Hubble law at later times. Without loss of generality, we model more realistically this transition with a smooth function. We predict a distinct pair-wise relationship between power-law exponent and particle interactions: for a given cosmology with negative (positive) exponent, smaller (larger) cross sections are required to reproduce the data. Lastly, via Bayesian methods, we quantify the epistemic uncertainty of theoretical parameters found in inverse problems.
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