发表机构
Center for Integrative Petroleum Research, King Fahd University of Petroleum and Minerals; Algorithmiq S.r.l.（法赫德国王石油与矿业大学综合石油研究中心; Algorithmiq有限责任公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出Learned AMDI，用强化学习训练共享局部策略替代固定选择准则，在保持层次约束下实现自适应细化，显著降低参考差异并提升占用率，且策略可迁移至更高分辨率。
AI 中文摘要
自适应多分辨率方法通过将细尺度自由度集中在需要的地方来降低表示成本，但其树更新通常由固定的局部准则控制。我们引入了学习型自适应多分辨率扩散成像（Learned AMDI），该方法保留了AMDI固定树传播器和层次约束，同时用通过近端策略优化训练的共享局部策略替代了传播后的选择器。回归测试表明，当使用相同的树时，能重现确定性AMDI轨迹至机器精度。在本文研究的Haar实现中，确定性单步选择器在54个决策中不接受任何细化。在九个保留案例中，Learned AMDI执行了393次细化，并将平均终端参考差异从0.17496降低到0.13657，同时占用率从0.13737上升到0.26660。逐步诊断显示偶尔会出现小的自适应能量增加；因此，固定树的能量稳定性并不能保证学习型外部迭代的单调性。在相当的占用率下，经过验证调整的观测细节阈值达到了0.13792的差异，且RMSE和SSIM略优，使两种方法基本处于相同的精度-占用率权衡曲线上。仅决策1的对照达到了0.13742，表明在此静态基准上大部分改进源于初始分配。共享演员无需重新训练即可迁移到64×64和128×128图像，相对于确定性AMDI改善了参考差异、RMSE和SSIM，而冻结阈值规则仍具有竞争力。因此，Learned AMDI提供了一种受层次约束、可跨分辨率迁移的自适应分配机制，并阐明了顺序决策的贡献。
英文摘要
Adaptive multiresolution methods reduce representation cost by concentrating fine-scale degrees of freedom where needed, but their tree updates are usually governed by fixed local criteria. We introduce Learned Adaptive Multiresolution Diffusion Imaging (Learned AMDI), which preserves the AMDI fixed-tree propagator and hierarchy constraints while replacing the post-propagation selector with a shared local policy trained by proximal policy optimization. Regression tests reproduce deterministic AMDI trajectories to machine precision when identical trees are used. In the Haar implementation studied here, the deterministic one-step selector accepts no refinements in 54 decisions. Across nine held-out cases, Learned AMDI executes 393 refinements and reduces the mean terminal reference discrepancy from $0.17496$ to $0.13657$, while occupancy rises from $0.13737$ to $0.26660$. Step-resolved diagnostics reveal occasional small adaptation-energy increases; fixed-tree energy stability therefore does not guarantee monotonicity of the learned outer iteration. At comparable occupancy, a validation-tuned observed-detail threshold reaches a discrepancy of $0.13792$ with slightly better RMSE and SSIM, placing both methods on essentially the same accuracy--occupancy tradeoff. A decision-1-only control reaches $0.13742$, indicating that most of the improvement on this static benchmark arises from the initial allocation. The shared actor transfers without retraining to $64\times64$ and $128\times128$ images, improving reference discrepancy, RMSE, and SSIM relative to deterministic AMDI, while the frozen threshold rule remains competitive. Learned AMDI thus provides a hierarchy-constrained, resolution-transferable mechanism for adaptive allocation and clarifies the contribution of sequential decisions.
