From 26130cde5701f478dc91f83b97de31eb3245bff9 Mon Sep 17 00:00:00 2001 From: NT Date: Tue, 20 Apr 2021 21:59:16 +0800 Subject: [PATCH] update cconv examples --- others-lagrangian.md | 19 ++++++++++--------- others-timeseries.md | 1 - resources/others-lagrangian-cconv-dfsph.jpg | Bin 0 -> 92868 bytes 3 files changed, 10 insertions(+), 10 deletions(-) create mode 100644 resources/others-lagrangian-cconv-dfsph.jpg diff --git a/others-lagrangian.md b/others-lagrangian.md index d8fca52..0d4c194 100644 --- a/others-lagrangian.md +++ b/others-lagrangian.md @@ -8,6 +8,7 @@ While the previous examples have focused on aspects beyond discretization (and used Cartesian grids as a placeholder), the following chapter will target scenarios where learning with dynamically changing and adaptive discretization has a benefit. + ## Types of computational meshes Generally speaking, we can distinguish three types of computational meshes (or "grids") @@ -27,6 +28,13 @@ for using stable, established DL components (especially regular convolutional la However, for target functions that exhibit an uneven mix of smooth and complex regions, the other two mesh types can have advantages. +```{figure} resources/others-lagrangian-cconv-dfsph.jpg +--- +name: others-lagrangian-cconv-dfsph +--- +Lagrangian simulations of liquids: the sampling points move with the material, and undergo large changes. In the +top row timesteps of a learned simulation, in the bottom row the traditional SPH solver. +``` ## Unstructured meshes and graph neural networks @@ -65,14 +73,6 @@ gives an indicator for how a method works. In the following, we will discuss an example targeting splashing liquids as a particularly challenging case. For these simulations, the fluid material moves significantly and is often distributed very non-uniformly. -```{figure} resources/others-lagrangian-environment.jpg ---- -name: others-lagrangian-environment ---- -An example of a particle-based liquid spreading in a landscape scenario, simulated with -learned approach using continuous convolutions {cite}`ummenhofer2019contconv`. -``` - The general outline of a learned, particle-based simulation is similar to a DL method working on a Cartesian grid: we store data such as the velocity at certain locations, and then repeatedly perform convolutions to create @@ -165,7 +165,8 @@ then supports optimization via gradient descent, e.g., w.r.t. input parameters s --- name: others-lagrangian-canyon --- -Another example of the learned particle-based liquid solver with a more complex ground geometry. +An example of a particle-based liquid spreading in a landscape scenario, simulated with +learned approach using continuous convolutions {cite}`ummenhofer2019contconv`. ``` ## Source code diff --git a/others-timeseries.md b/others-timeseries.md index 15a468c..f587fcb 100644 --- a/others-timeseries.md +++ b/others-timeseries.md @@ -21,7 +21,6 @@ the encoder/decoder of Kim et al. {cite}`bkim2019deep`. ```{figure} resources/others-timeseries-lsp-overview.jpg --- -height: 200px name: timeseries-lsp-overview --- For time series predictions with ROMs, we encode the state of our system with an encoder $f_e$, predict diff --git a/resources/others-lagrangian-cconv-dfsph.jpg b/resources/others-lagrangian-cconv-dfsph.jpg new file mode 100644 index 0000000000000000000000000000000000000000..34032d96c31b7c634a6e54e297e6ce1b7aa8261b GIT binary patch literal 92868 zcmeFYbzD_l_b6GpkkS>u1C6q=|6eI0a`Me9R2fAc^A-~kdq`^{qx-cc7= zGph9OJ1j90zyzO2z;rJU`iC2%AP@G3hN9j93I<9D1b8>F^|rTn_i^&@y?Bq!dXY1j{A875#FUTjr4@k=edRp7M*!wct*gGQKWtcy=cQP{~?PQou zM6?97JeBO7kZQr+_6EV)hPJ^jwi0&CaYMTXf_OP5i}!`q%wluv+9fEg_9ZRa4Ve@*3gS@21Q`FAG+0s{B~g!w$Y 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