diff --git a/Yunlin_Zeng2024SEG/figs/framework.png b/Yunlin_Zeng2024SEG/figs/framework.png new file mode 100644 index 0000000..8cdc04a Binary files /dev/null and b/Yunlin_Zeng2024SEG/figs/framework.png differ diff --git a/Yunlin_Zeng2024SEG/figs/result.png b/Yunlin_Zeng2024SEG/figs/result.png new file mode 100644 index 0000000..70ac441 Binary files /dev/null and b/Yunlin_Zeng2024SEG/figs/result.png differ diff --git a/Yunlin_Zeng2024SEG/paper.bib b/Yunlin_Zeng2024SEG/paper.bib new file mode 100644 index 0000000..7579896 --- /dev/null +++ b/Yunlin_Zeng2024SEG/paper.bib @@ -0,0 +1,50 @@ +@article{Jones2012, + author = "E. Jones, C. and A. Edgar, J. and I. Selvage, J. and Crook, H.", + title = "Building Complex Synthetic Models to Evaluate Acquisition Geometries and Velocity Inversion Technologies", + journal= "", + year = "2012", + volume = "", + number = "", + pages = "", + doi = "https://doi.org/10.3997/2214-4609.20148575", + url = "https://www.earthdoc.org/content/papers/10.3997/2214-4609.20148575", + publisher = "European Association of Geoscientists & Engineers", + issn = "2214-4609", + type = "", + eid = "cp-293-00580", + } + +@conference {orozco2022SPIEadjoint, + title = {Adjoint operators enable fast and amortized machine learning based Bayesian uncertainty quantification}, + booktitle = {SPIE Medical Imaging Conference}, + year = {2023}, + note = {(SPIE, San Diego)}, + month = {02}, + abstract = {Machine learning algorithms such as Normalizing Flows, VAEs, and GANs are powerful tools in Bayesian uncertainty quantification (UQ) of inverse problems. Unfortunately, when using these algorithms medical imaging practitioners are faced with the challenging task of manually defining neural networks that can handle complicated inputs such as acoustic data. This task needs to be replicated for different receiver types or configurations since these change the dimensionality of the input. We propose to first transform the data using the adjoint operator {\textemdash}ex: time reversal in photoacoustic imaging (PAI) or back-projection in computer tomography (CT) imaging {\textemdash} then continue posterior inference using the adjoint data as an input now that it has been standardized to the size of the unknown model. This adjoint preprocessing technique has been used in previous works but with minimal discussion on if it is biased. In this work, we prove that conditioning on adjoint data is unbiased for a certain class of inverse problems. We then demonstrate with two medical imaging examples (PAI and CT) that adjoints enable two things: Firstly, adjoints partially undo the physics of the forward operator resulting in faster convergence of an ML based Bayesian UQ technique. Secondly, the algorithm is now robust to changes in the observed data caused by differing transducer subsampling in PAI and number of angles in CT. Our adjoint-based Bayesian inference method results in point estimates that are faster to compute than traditional baselines and show higher SSIM metrics, while also providing validated UQ.}, + keywords = {Amortized Inference, Bayesian inference, deep learning, Inverse problems, machine learning, medical imaging, Normalizing flows, SPIE, Uncertainty quantification}, + url = {https://slim.gatech.edu/Publications/Public/Conferences/SPIE/2023/orozco2022SPIEadjoint/SPIE_2022_adjoint.html}, + author = {Rafael Orozco and Ali Siahkoohi and Gabrio Rizzuti and Tristan van Leeuwen and Felix J. Herrmann} +} + +@misc{yin2023wise, + title={WISE: full-Waveform variational Inference via Subsurface Extensions}, + author={Ziyi Yin and Rafael Orozco and Mathias Louboutin and Felix J. Herrmann}, + year={2023}, + eprint={2401.06230}, + archivePrefix={arXiv}, + primaryClass={physics.geo-ph} +} + +@article{Cranmer2020, + title={The frontier of simulation-based inference}, + volume={117}, + ISSN={1091-6490}, + url={http://dx.doi.org/10.1073/pnas.1912789117}, + DOI={10.1073/pnas.1912789117}, + number={48}, + journal={Proceedings of the National Academy of Sciences}, + publisher={Proceedings of the National Academy of Sciences}, + author={Cranmer, Kyle and Brehmer, Johann and Louppe, Gilles}, + year={2020}, + month=may, pages={30055–30062} } + diff --git a/Yunlin_Zeng2024SEG/paper.qmd b/Yunlin_Zeng2024SEG/paper.qmd new file mode 100644 index 0000000..1d1f3b1 --- /dev/null +++ b/Yunlin_Zeng2024SEG/paper.qmd @@ -0,0 +1,38 @@ +--- +title: "Enhancing Full-Waveform Variational Inference through Stochastic Resampling and Data Augmentation" +author: + - name: + Yunlin Zeng^1^, Rafael Orozco^1^, Ziyi Yin^1^, Felix Herrmann ^1^ \ + + ^1^ Georgia Institute of Technology + +bibliography: paper.bib +--- + +## Introduction + +Full-Waveform Inversion (FWI) corresponds to a computationally expensive iterative optimization scheme that determines migration-velocity models by minimizing the discrepancy between observed seismic shot data and data generated by a forward model parameterized by the velocity. Recent advancements, such as full-Waveform variational Inference via Subsurface Extensions (WISE, @yin2023wise) in simulation-based inference [@Cranmer2020], produce amortized neural posterior estimates that enable fast online inference of the velocity. These neural approximations to the posterior distribution, $p_{\boldsymbol{\theta}}(\mathbf{x}\vert\mathbf{y})\approx p(\mathbf{x}\vert\mathbf{y})$ with $\mathbf{x}$, the velocity model, $\mathbf{y}$, the shot data, and $\boldsymbol{\theta}$, the network weights, are obtained with variational inference, which requires extensive off-line training. Aside from providing statistically robust estimates via the conditional mean, $\mathbb{E}_{\mathbf{x}\sim p_{\boldsymbol{\theta}}(\mathbf{x}\vert\mathbf{y})}(\mathbf{x})$, these neural posterior also provide a useful metric of the uncertainty in terms of the variance $\mathbb{V}_{\mathbf{x}\sim p_{\boldsymbol{\theta}}(\mathbf{x}\vert\mathbf{y})}(\mathbf{x})$. To make this amortized inference approach computationally feasible, we follow @yin2023wise and train on pairs $\left\{(\mathbf{x}^{(m)}, \mathbf{\bar{y}}^{(m)})\right\}_{m=1}^M$, where the $\mathbf{\bar{y}}^{(m)}$ stand for subsurface-offset Common Image Gathers, computed from each shot dataset, $\mathbf{y}^{(m)}$. While CIG's as *physics-based summary statistics* are better suited to inform the posterior than plain migration---i.e, they preserve information even when the migration-velocity model is poor, their performance still depends on the choice of the initial migration-velocity model, $\mathbf{x}_0$. During this talk, we will study the impact of varying initial background-velocity models on the quality of the amortized neural posterior sampler. We will also investigate how augmenting the training set with different initial background-velocity models can lead to improved performance. + +## Methodology + +By interpreting the initial migration-velocity model as stochastic latent variables---i.e., $\mathbf{x}_0\sim p(\mathbf{x}_0\vert \mathbf{x})$ with $\mathbf{x}\sim p(\mathbf{x})$, we propose to augment the training pairs, $\left\{(\mathbf{x}^{(m)}, \mathbf{\bar{y}}^{(m)})\right\}_{m=1}^M$, with $\mathbf{\bar{y}}^{(m)}$'s computed for one single initial migration-velocity model, $\mathbf{x}_0$, with $\mathbf{\bar{y}}^{(m)}$, obtained with multiple different (randomly perturbed) initial migration-velocity models, $\mathbf{x}_0\sim p(\mathbf{x}_0\vert \mathbf{x})$. The aim of this training dataset augmentation is to improve the robustness of WISE---i.e., make its neural posterior estimation less dependent on the choice for the initial migration-velocity model, $\mathbf{x}_0$. + +## Results + +To improve the neural posterior estimation's robustness, multiple initial migration-velocity models, $\mathbf{x}_0$, are obtained by randomly perturbing the ground-truth velocity model, $\mathbf{x}$, followed by extensive smoothing. Since this deformation is stochastic, we can sample an "infinite" number of background models, $\mathbf{x}_0\sim p(\mathbf{x}_0\vert \mathbf{x})$, to be used during training, although in practice we regenerate the background model a few times ($3-5$) (Figure 1(a)). Then, new $\mathbf{\bar{y}}^{(i)}$ are generated based on each $\mathbf{x}_0^{(i)}$ and $\mathbf{y}$ (Figure 1(b)), and the resulting $\{\mathbf{x}, \mathbf{\bar{y}}^{(i)}\}$ pairs form a training dataset for the Conditional Normalizing Flow (CNF) (Figure 1(c)). + +To evaluate our method, we divide the Compass model dataset [@Jones2012] by allocating $800$ pairs for training and $150$ for testing. We train the baseline CNF on $M=800$ velocity-extended image pairs, and train enhanced CNFs on augmented training pairs ($M=1600, 2400, ...$ etc.). The trained CNFs are evaluated by structural similarity index measure (SSIM) and root mean square error (RMSE) of the posterior samples' mean against the ground truth. SSIM improves from $0.725$ to $0.753$ while RMSE improves from $0.110$ to $0.107$ on $150$ unseen test samples. Figure 2 shows the conditional mean and point-wise standard deviation of the baseline and the enhanced CNF posterior samples, where the enhanced CNF sampler aligns more closely with the ground truth. We observe the trend that the uncertainty is reduced as we increase the number of background-velocity model regenerations during training. This implies that the uncertainty information in the baseline has yet not captured the uncertainty fully due to the choice of a fixed background-velocity model while our method has learned to incorporate this uncertainty information into the final inference result. + +::: {#fig-framwork} +![](./figs/framework.png){width="90%"} + +The complete stochastic resampling framework: (a) Randomly perturbed and smoothed velocity models, $\mathbf{x}$, to get new background models, $\mathbf{x}_0\sim p(\mathbf{x}_0\vert \mathbf{x})$. (b) Generate $\mathbf{\bar{y}}$ based on $\mathbf{x}_0$ and seismic shot data $\mathbf{y}$. (c) Train the CNF on $\{\mathbf{x}, \mathbf{\bar{y}}\}$ pairs. +::: + +::: {#fig-result} +![](./figs/result.png){width="90%"} + +Comparison of conditional mean and point-wise standard deviation between the enhanced CNF and the baseline CNF. +::: + +## Reference diff --git a/_quarto.yml b/_quarto.yml index ee1ddf5..6efad97 100644 --- a/_quarto.yml +++ b/_quarto.yml @@ -24,6 +24,8 @@ website: text: "Velocity Continuation for Common Image Gathers" - file: erdinc2024SEG/abstract.qmd text: "Building subsurface velocity priors from field observations" + - file: Yunlin_Zeng2024SEG/paper.qmd + text: "Enhancing Full-Waveform Variational Inference through Stochastic Resampling and Data Augmentation" page-footer: center: - file: license.qmd diff --git a/index.qmd b/index.qmd index de263f3..3f7a8d0 100644 --- a/index.qmd +++ b/index.qmd @@ -11,4 +11,5 @@ List of abstracts: - [VelGen](erdinc2024SEG/abstract.qmd): Building subsurface velocity priors from field observations - [Velocity Continuation for Common Image Gathers with Fourier Neural Operators](Rex2024SEG/paper.qmd) A framework to accelerate migration-velocity analysis and uncertainty quantification - [Digital twin with control](GahlotLi2024SEG/paper.qmd) A Digital Twin for Geological Carbon Storage with Controlled Injectivity -- [WISER](yin2024SEG/paper.qmd): full-Waveform variational Inference via Subsurface Extensions with Refinements \ No newline at end of file +- [WISER](yin2024SEG/paper.qmd): full-Waveform variational Inference via Subsurface Extensions with Refinements +- [Stochastic resampling](Yunlin_Zeng2024SEG/paper.qmd): Enhancing Full-Waveform Variational Inference through Stochastic Resampling and Data Augmentation