Learning a continuous and reliable representation of physical fields from
sparse sampling is challenging and it affects diverse scientific disciplines.
In a recent work, we present a novel model called MMGN (Multiplicative and
Modulated Gabor Network) with implicit neural networks. In this work, we design
additional studies leveraging explainability methods to complement the previous
experiments and further enhance the understanding of latent representations
generated by the model. The adopted methods are general enough to be leveraged
for any latent space inspection. Preliminary results demonstrate the contextual
information incorporated in the latent representations and their impact on the
model performance. As a work in progress, we will continue to verify our
findings and develop novel explainability approaches.

学习稀疏采样下的连续可靠物理场表示的挑战及其影响是多学科的。本文提出了一种名为 MMGN（乘法和调制 Gabor 网络）的新模型，采用隐式神经网络。我们设计了额外的研究来增强对模型生成的潜在表示的理解，并采用了解释性方法。初步结果显示潜在表示中融入的上下文信息以及其对模型性能的影响。作为正在进行的工作，我们将继续验证发现并发展新的解释性方法。

研究科学连续领域重建中潜在表示的影响

Studying the Impact of Latent Representations in Implicit Neural  Networks for Scientific Continuous Field Reconstruction

There is a growing gap between the impressive results of deep image
generative models and classical algorithms that offer theoretical guarantees.
The former suffer from mode collapse or memorization issues, limiting their
application to scientific data. The latter require restrictive assumptions such
as log-concavity to escape the curse of dimensionality. We partially bridge
this gap by introducing conditionally strongly log-concave (CSLC) models, which
factorize the data distribution into a product of conditional probability
distributions that are strongly log-concave. This factorization is obtained
with orthogonal projectors adapted to the data distribution. It leads to
efficient parameter estimation and sampling algorithms, with theoretical
guarantees, although the data distribution is not globally log-concave. We show
that several challenging multiscale processes are conditionally log-concave
using wavelet packet orthogonal projectors. Numerical results are shown for
physical fields such as the $\varphi^4$ model and weak lensing convergence maps
with higher resolution than in previous works.

介绍了条件强对数凹模型的概念，该模型将数据分布因子化为强对数凹条件概率分布的乘积，并使用适应于数据分布的正交投影器来实现因子化，从而实现了有效的参数估计和抽样算法，并在物理字段等多个领域展示了该模型的实用性。