Current hydrological modeling methods combine data-driven Machine Learning
(ML) algorithms and traditional physics-based models to address their
respective limitations incorrect parameter estimates from rigid physics-based
models and the neglect of physical process constraints by ML algorithms.
Despite the accuracy of ML in outcome prediction, the integration of scientific
knowledge is crucial for reliable predictions. This study introduces a Physics
Informed Machine Learning (PIML) model, which merges the process understanding
of conceptual hydrological models with the predictive efficiency of ML
algorithms. Applied to the Anandapur sub-catchment, the PIML model demonstrates
superior performance in forecasting monthly streamflow and actual
evapotranspiration over both standalone conceptual models and ML algorithms,
ensuring physical consistency of the outputs. This study replicates the
methodologies of Bhasme, P., Vagadiya, J., & Bhatia, U. (2022) from their
pivotal work on Physics Informed Machine Learning for hydrological processes,
utilizing their shared code and datasets to further explore the predictive
capabilities in hydrological modeling.

该研究介绍了一种物理信息驱动的机器学习（PIML）模型，将概念性水文模型的过程理解与机器学习算法的预测效能相结合，在安纳达普尔亚分水汇中应用，表明该模型在预测月流量和实际蒸散发方面的性能优于独立的概念模型和机器学习算法，确保输出的物理一致性。

复制研究：物理引导的机器学习增强水文模型

Replication Study: Enhancing Hydrological Modeling with Physics-Guided  Machine Learning

Amortized variational inference produces a posterior approximator that can
compute a posterior approximation given any new observation. Unfortunately,
there are few guarantees about the quality of these approximate posteriors. We
propose Conformalized Amortized Neural Variational Inference (CANVI), a
procedure that is scalable, easily implemented, and provides guaranteed
marginal coverage. Given a collection of candidate amortized posterior
approximators, CANVI constructs conformalized predictors based on each
candidate, compares the predictors using a metric known as predictive
efficiency, and returns the most efficient predictor. CANVI ensures that the
resulting predictor constructs regions that contain the truth with high
probability (exactly how high is prespecified by the user). CANVI is agnostic
to design decisions in formulating the candidate approximators and only
requires access to samples from the forward model, permitting its use in
likelihood-free settings. We prove lower bounds on the predictive efficiency of
the regions produced by CANVI and explore how the quality of a posterior
approximation relates to the predictive efficiency of prediction regions based
on that approximation. Finally, we demonstrate the accurate calibration and
high predictive efficiency of CANVI on a suite of simulation-based inference
benchmark tasks and an important scientific task: analyzing galaxy emission
spectra.

CANVI 是一种可扩展、易于实施且具有保证边际覆盖率的方法，可以通过对每个候选者构建经过确认的预测模型、比较预测效率并返回最有效的预测器来构建后验概率逼近程序，同时不需要对候选逼近器的设计决策进行考虑，在没有似然函数的情况下使用 CANVI，我们对 CANVI 所产生的预测区域的预测效率进行了下界证明，并探讨了后验概率逼近质量与基于该逼近的预测区域的预测效率之间的关系，最后，在一系列基于模拟的推断基准任务以及一个重要的科学任务（分析恒星发射光谱）中，我们展示了 CANVI 的精确校准和高预测效率。

具有覆盖保障的变分推断

Variational Inference with Coverage Guarantees

This note introduces the method of cross-conformal prediction, which is a
hybrid of the methods of inductive conformal prediction and cross-validation,
and studies its validity and predictive efficiency empirically.

介绍了交叉一致性预测方法，它是归纳一致性预测和交叉验证方法的混合，经验上研究了它的有效性和预测效率。