From e3e72982a7e7789ff620d49baaa2bf80fa5a4c18 Mon Sep 17 00:00:00 2001 From: NT Date: Tue, 26 Jan 2021 13:04:57 +0800 Subject: [PATCH] intro update --- intro.md | 36 +++++++++++++-------------- overview.md | 67 ++++++++++++++++++++++++++++++-------------------- references.bib | 51 ++++++++++++++++++++++++++++++++++++++ 3 files changed, 110 insertions(+), 44 deletions(-) diff --git a/intro.md b/intro.md index 121cf97..9c888a4 100644 --- a/intro.md +++ b/intro.md @@ -9,6 +9,7 @@ As much as possible, the algorithms will come with hands-on code examples to qui Beyond standard _supervised_ learning from data, we'll look at loss constraints, and more tightly coupled learning algorithms with differentiable simulations. + ```{figure} resources/teaser.png --- height: 220px @@ -51,9 +52,9 @@ immediately see what happens -- give it a try... Oh, and it's great because it's [literate programming](https://en.wikipedia.org/wiki/Literate_programming). ``` -## Specifically +## More Specifically -To be a bit more specific, _physics_ is a huge field, we can't cover everything... +To be a bit more specific, _physics_ is a huge field, and we can't cover everything... ```{note} For now our focus is: @@ -69,16 +70,13 @@ For now our focus is: The contents of the following files would not have been possible without the help of many people. Here's an alphabetical list. Big kudos to everyone 🙏 -- Mr. X -- Ms. y -- ... +- [Li-wei Chen](https://ge.in.tum.de/about/dr-liwei-chen/) +- [Philipp Holl](https://ge.in.tum.de/about/) +- [Patrick Schnell](https://ge.in.tum.de/about/patrick-schnell/) +- [Nils Thuerey](https://ge.in.tum.de/about/n-thuerey/) +- [Kiwon Um](https://ge.in.tum.de/about/kiwon/) - - - - - -% some markdown tests follow ... + --- -## Planned content +## TODOs , Planned content Loose collection of notes and TODOs: General physics & dl , intro & textual overview -- Intro phys loss example, notebook patrick +- Intro phys loss example, parabola example -Supervised? Airfoils? Liwei, simple example? app: optimization, shape opt w surrogates +Supervised simple starting point - AIAA supervised learning , idp_weissenov/201019-upd-arxiv-v2/ {cite}`thuerey2020deepFlowPred` skepticism? , started colab -> https://colab.research.google.com/drive/11KUe5Ybuprd7_qmNTe1nvQVUz3W6gRUo torch version 1.7 [upd from Liwei?] -vs. PINNs [alt.: neural ODEs , PDE net?] , all using GD (optional, PINNs could use BFGS) +- surrogates, shape opt? + +Physical losses + +- vs. PINNs [alt.: neural ODEs , PDE net?] , all using GD (optional, PINNs could use BFGS) [PINNs], phiflow example -> convert to colab - PINNs -> are unsupervised a la tompson; all DL NNs are "supervised" during learning, unsup just means not precomputed and goes through function @@ -120,7 +122,6 @@ vs. PINNs [alt.: neural ODEs , PDE net?] , all using GD (optional, PINNs could u - discuss CG solver, tompson as basic ''unsupervisedd'' example? Diff phys, start with overview of idea: gradients via autodiff, then run GD - (TODO include squared func Patrick?) - illustrate and discuss gradients -> mult. for chain rule; (later: more general PG chain w func composition) @@ -164,4 +165,3 @@ _Misc jupyter book TODOs_ - Fix latex PDF output - How to include links to papers in the bibtex references? - diff --git a/overview.md b/overview.md index 99740ad..27dd006 100644 --- a/overview.md +++ b/overview.md @@ -10,34 +10,46 @@ active, quickly growing and exciting field of research -- we want to provide a starting point for new researchers as well as a hands-on introduction into state-of-the-art resarch topics. + +```{figure} resources/overview-pano.jpg +--- +height: 240px +name: overview-pano +--- +Understanding our environment, and predicting how it will evolve is one of the key challenges of humankind. +``` + ## Motivation -From weather forecasts (? ) over X, Y, -... more ... -to quantum physics (? ), +From weather and climate forecasts {cite}`stocker2014climate`, +over quantum physics {cite}`o2016scalable`, +to the control of plasma fusion {cite}`maingi2019fesreport`, using numerical analysis to obtain solutions for physical models has become an integral part of science. At the same time, machine learning technologies and deep neural networks in particular, -have led to impressive achievements in a variety of field. -Among others, GPT-3 -has recently demonstrated that learning methods can -achieve astounding accuracy for processing natural language. -Also: AlphaGO, closer to physics: protein folding... -This is a vibrant, quickly developing field with vast possibilities. +have led to impressive achievements in a variety of fields: +from image classification {cite}`krizhevsky2012` over +natural language processing {cite}`radford2019language`, +and more recently also for protein folding {cite}`alquraishi2019alphafold`. +The field is very vibrant, and quickly developing, with the promise of vast possibilities. -The successes of DL approaches have given rise to concerns that this technology has +At the same time, the successes of deep learning (DL) approaches +has given rise to concerns that this technology has the potential to replace the traditional, simulation-driven approach to science. Instead of relying on models that are carefully crafted from first principles, can data collections of sufficient size be processed to provide the correct answers instead? +In short: this concern is unfounded. As we'll show in the next chapters, +it is crucial to bring together both worlds: _classical numerical techniques_ +and _deep learning_. -Very clear advantages of data-driven approaches would lead -to a "yes" here ... but that's not where we stand as of this writing. -Given the current state of the art, these clear breakthroughs -are outstanding, the proposed techniques are novel, +One central reason for the importance of this combination is +that DL approaches are simply not powerful enough by themselves. +Given the current state of the art, the clear breakthroughs of DL +in physical applications are outstanding, the proposed techniques are novel, sometimes difficult to apply, and -significant difficulties combing physics and DL persist. +significant practical difficulties combing physics and DL persist. Also, many fundamental theoretical questions remain unaddressed, most importantly regarding data efficienty and generalization. @@ -47,22 +59,23 @@ been developed to solve fundamental model equations such as the Navier-Stokes, Maxwell’s, or Schroedinger’s equations. Seemingly trivial changes to the discretization can determine whether key phenomena are visible in the solutions or not. +Rather than discarding the powerful methods that have been +carefully developed in the field of numerical mathematics, it +is highly beneficial for DL to use them as much as possible. -```{admonition} Goal of this document +```{admonition} Goals of this document :class: tip -Thus, a key aspect that we want to address in the following in the following is: +Thus, the key aspects that we want to address in the following are: - explain how to use DL, -- how to combine it with existing knowledge of physics and simulations, -- **without throwing away** all existing numerical knowledge and techniques! +- and how to combine it with existing knowledge of physics and simulations, +- **without throwing away** all existing numerical knowledge and techniques. ``` -Rather, we want to build on all the neat techniques that we have -at our disposal, and use them as -much as possible. I.e., our goal is to _reconcile_ the data-centered +Thus, we want to build on all the powerful techniques that we have +at our disposal, and use them wherever we can. +I.e., our goal is to _reconcile_ the data-centered viewpoint and the physical simuation viewpoint. -Also interesting: from a math standpoint ... -''just'' non-linear optimization ... ## Categorization @@ -124,8 +137,9 @@ each of the different techniques is particularly useful. A brief look at our _Notation_ won't hurt in both cases, though! ``` +--- -## A brief history of PBDL in the context of Fluids + ## Deep Learning and Neural Networks @@ -160,4 +174,5 @@ we only deal with _regression_ problems in the following. maximum likelihood estimation +Also interesting: from a math standpoint ''just'' non-linear optimization ... diff --git a/references.bib b/references.bib index 3e14d58..be1bf9a 100644 --- a/references.bib +++ b/references.bib @@ -787,9 +787,60 @@ publisher={Elsevier} } +@book{stocker2014climate, + title={Climate change 2013: the physical science basis: Working Group I contribution to the Fifth assessment report of the Intergovernmental Panel on Climate Change}, + author={Stocker, Thomas}, + year={2014}, + publisher={Cambridge university press} +} +@article{maingi2019fesreport, + title={Summary of the FESAC transformative enabling capabilities panel report}, + author={Maingi, Rajesh and Lumsdaine, Arnold and Allain, Jean Paul and Chacon, Luis and Gourlay, SA and others}, + journal={Fusion Science and Technology}, + volume={75}, + number={3}, + pages={167--177}, + year={2019}, + publisher={Taylor Francis} +} +@article{o2016scalable, + title={Scalable quantum simulation of molecular energies}, + author={O’Malley, Peter JJ and Babbush, Ryan and Kivlichan, Ian D and Romero, Jonathan and McClean, Jarrod R and Barends, Rami and Kelly, Julian and Roushan, Pedram and Tranter, Andrew and Ding, Nan and others}, + journal={Physical Review X}, + volume={6}, + number={3}, + pages={031007}, + year={2016}, + publisher={APS} +} +@inproceedings{krizhevsky2012, + title = {ImageNet Classification with Deep Convolutional Neural Networks}, + author = {Alex Krizhevsky and Sutskever, Ilya and Hinton, Geoffrey E}, + booktitle = {Advances in Neural Information Processing Systems}, + year =2012, +} +@article{radford2019language, + title={Language models are unsupervised multitask learners}, + author={Radford, Alec and Wu, Jeffrey and Child, Rewon and Luan, David and Amodei, Dario and Sutskever, Ilya}, + journal={OpenAI blog}, + volume={1}, + number={8}, + pages={9}, + year={2019} +} +@article{alquraishi2019alphafold, + title={AlphaFold at CASP13}, + author={AlQuraishi, Mohammed}, + journal={Bioinformatics}, + volume={35}, + number={22}, + pages={4862--4865}, + year={2019}, + publisher={Oxford University Press} +}