CSympNet-ID：用于线性阻尼哈密顿系统的共形辛映射学习
CSympNet-ID: conformal-symplectic map learning for linearly damped Hamiltonian systems
AI总结：
针对线性阻尼哈密顿系统，提出CSympNet-ID框架，直接从快照对学习一步流映射，通过构建保证离散共形辛性，其架构含辛神经核心与缩放层，给出相关因式分解及密度结果，实验效果良好。
摘要：
从离散观测中学习耗散动力学对于可靠的长期预测和有物理意义的参数识别至关重要。对于线性阻尼哈密顿系统，精确流通常不是辛的而是共形辛的。我们提出了具有阻尼识别的共形辛网络（CSympNet-ID），一个离散时间映射学习框架，它直接从快照对中学习一步流映射，同时通过构造强制实现精确的离散共形辛性，无需惩罚项或投影。该架构由一个精确的辛神经核心和显式对角缩放层组成，其因子由标量阻尼率参数指数化参数化，从而保证了学习到的耗散因子的正性和可解释性。我们为共形辛映射建立了缩放共轭因式分解，并为CSympNet-ID推导了逐点步长密度结果。我们评估了一个不规则步长阻尼振荡器、一个阻尼弹簧质量链、一个阻尼非线性立方振荡器以及其他高维扩展。在报告的实验中，CSympNet-ID在比较模型中给出了最有利的总体结果，特别是在数据稀缺的情况下、目标收缩律恢复以及非结构化基线迅速退化的高维测试中。
英文摘要：
Learning dissipative dynamics from discrete observations is essential for reliable long-horizon prediction and physically meaningful parameter identification. For linearly damped Hamiltonian systems, the exact flow is generally not symplectic but conformally symplectic, contracting the canonical symplectic form by a scalar factor that reflects the net dissipation. We propose Conformal Symplectic Networks with damping identification (CSympNet-ID), a discrete-time map-learning framework that learns the one-step flow map directly from snapshot pairs while enforcing exact discrete conformal symplecticity by construction, without penalty terms or projection. The architecture composes an exact symplectic neural core with explicit diagonal scaling layers whose factors are parameterized exponentially by a scalar damping-rate parameter, thereby guaranteeing positivity and interpretability of the learned dissipation factor. We establish a scaling-conjugacy factorization for conformal symplectic maps and derive a pointwise-in-step density result for CSympNet-ID. We evaluate an irregular-step damped oscillator, a damped spring-mass chain, a damped nonlinear cubic oscillator, and additional high-dimensional extensions. CSympNet-ID gives the most favorable overall results among the compared models in the reported experiments, particularly in data-scarce regimes, target contraction-law recovery, and high-dimensional tests where unstructured baselines degrade rapidly.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
