From 8fdf85c273e32ee5f835fee1299a6d40aeb6554f Mon Sep 17 00:00:00 2001 From: aver Date: Sat, 13 Apr 2024 17:09:18 +0100 Subject: [PATCH] Adding beltran-jimenez2024galerkin --- _news/galerkin-laplace-accepted.md | 7 ++++++ _publications/beltran-jimenez2024galerkin.md | 21 ++++++++++++++++++ .../beltran-jimenez2024galerkin/gala.png | Bin 0 -> 39648 bytes 3 files changed, 28 insertions(+) create mode 100644 _news/galerkin-laplace-accepted.md create mode 100644 _publications/beltran-jimenez2024galerkin.md create mode 100644 images/papers/beltran-jimenez2024galerkin/gala.png diff --git a/_news/galerkin-laplace-accepted.md b/_news/galerkin-laplace-accepted.md new file mode 100644 index 0000000..a3e3e63 --- /dev/null +++ b/_news/galerkin-laplace-accepted.md @@ -0,0 +1,7 @@ +--- +title: "Galerkin meets Laplace" +collection: news +permalink: /news/galerkin-laplace-accepted +date: 2024-03-05 +--- +We will present a work on fast uncertainty estimation for physics-inspired neural nets at the ICLR 2024 Workshop on AI4DifferentialEquations in Science. \ No newline at end of file diff --git a/_publications/beltran-jimenez2024galerkin.md b/_publications/beltran-jimenez2024galerkin.md new file mode 100644 index 0000000..5df092b --- /dev/null +++ b/_publications/beltran-jimenez2024galerkin.md @@ -0,0 +1,21 @@ +--- +collection: publications +ref: "beltran-jimenez2024galerkin" +permalink: "publications/beltran-jimenez2024galerkin" +title: "Galerkin meets Laplace: Fast uncertainty estimation in neural PDEs" +date: 2024-03-05 00:00 +tags: uq probml pinns +image: "/images/papers/beltran-jimenez2024galerkin/gala.png" +authors: "Christian Jimenez Beltran, Antonio Vergari, Aretha L Teckentrup, Konstantinos C. Zygalakis" +paperurl: "https://openreview.net/forum?id=HdzFecgdzB" +pdf: "https://openreview.net/pdf?id=HdzFecgdzB +venue: "AI4DifferentialEquations @ ICLR 2024" +excerpt: "We propose DeepGALA as a fast and effective way to estimate uncertainty in deep neural PDE solvers that allows us to capture meaningful uncertainty in out of domain of the PDE solution and in low data regimes with little overhead." +abstract: "The solution of partial differential equations (PDEs) by deep neural networks trained to satisfy the differential operator has become increasingly popular. While these approaches can lead to very accurate approximations, they tend to be over- confident and fail to capture the uncertainty around the approximation. In this work, we propose a Bayesian treatment to the deep Galerkin method (Sirignano & Spiliopoulos, 2018), a popular neural approach for solving parametric PDEs. In particular, we reinterpret the deep Galerkin method as the maximum a posteriori estimator corresponding to a likelihood term over a fictitious dataset, leading thus to a natural definition of a posterior. Then, we propose to model such posterior via the Laplace approximation, a fast approximation that allows us to capture mean- ingful uncertainty in out of domain interpolation of the PDE solution and in low data regimes with little overhead, as shown in our preliminary experiments." +bibtex: "@inproceedings{beltran-jimenez2024galerkin, + title={Galerkin meets Laplace: Fast uncertainty estimation in neural PDEs}, + author={Christian Jimenez Beltran, Antonio Vergari, Aretha L Teckentrup, Konstantinos C. Zygalakis}, + booktitle={ICLR 2024 Workshop on AI4DifferentialEquations}, + year={2024} +}" +--- diff --git a/images/papers/beltran-jimenez2024galerkin/gala.png b/images/papers/beltran-jimenez2024galerkin/gala.png new file mode 100644 index 0000000000000000000000000000000000000000..cf1fffa1d1afb608c24e7300bb7988931045a293 GIT binary patch literal 39648 zcmXt916XCz+RihRZP#RTa+7UyvNhRFnC!{6T_;9Sk`;|-YV!GZc6VzW zw#5+fzja-14_@Bf821EzS#epmS#cO7m~S{QEu{h3EYB5=f8*g{H5!P3IUgJxj89CQ zEA<{tW`;B~+vgx?WafXpQO0D{8@<@NxX}^gz1a8{0mv>ZIW2PK~FOcNu0r>wNc_tI{9Odb^?Yd4FDa z9cCtXE{>BkI$vu)$`uWt5e>&I;o{<2UClr=dVRV*TBtEn&7L$_tTnOp@bGB8*VoZm z+385rG968xJm?_wzL``zC;R%fVAXr>@5qSq{=bYeh$GsnwkgAB-`8XPqhw~I)YGJ* zqN1ne^*1$HY3bIpw+0b8xhS81XRED^)6tX`=|t}jgEZM<;^MAL%>3^!ju;BT@Hn}I zd>-}FQDlm$humi(Q3N~#sq9u@8a0N{9UUF3D|yG1BqYCzGCjgZM`f&SY&2_)zp$E) z60@?#pLaY1!(A@+((K}5V!8@t)9js`tgo5TMM>!B%KKe{f`ZU7F(H_ok7g+Dp?_Fe zNlQpb)IHZVw7-pPcKw3%x?go|YH7KO&w9xpauLgmP15rS?R?o~#EujL8;Hak{6npb 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