Frameworks for Modeling and Inversion
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1 Frameworks for Modeling and Inversion William W. Symes The Rice Inversion Project Department of Computational and Applied Mathematics Rice University, Houston, TX 7 June 2012 Open Source E+P Software 1
2 Project Goal: Aid rapid prototyping of new wave modeling, inversion apps wave physics, modeling methods, optimization algorithms, hardware & software environments without starting from scratch every time Find the right abstractions and data structures, create a proof-of-concept open source implementation 7 June 2012 Open Source E+P Software 2
3 Components Modeling IWAVE Optimization RVL Inversion IWAVE++ 7 June 2012 Open Source E+P Software 3
4 Framework for Wave Modeling [IWAVE] 7 June 2012 Open Source E+P Software 4
5 Why a framework? FD, FE apps share many common tasks: Grid allocation Data exchange patterns (domain decomposition) depend on scheme i/o w. common file structures (SEGY/SU, RSF, ) Many of these reusable across many apps, given interfaces and task def ns Unstructured-mesh FEM frameworks (mostly CFDoriented): PETSc, DUNE, deal.ii, FEniCS, Trilinos, Regular grid FD/FE TD: restricted domain - additional opportunities for re-use, efficient implementation 7 June 2012 Open Source E+P Software 5
6 Basic Data Structures for FDTD Regular grid methods: Arrays = fcns on rectangular subsets of infinite lattice, virtual sub-arrays Every virtual sub-array carries reference to parent allocated array Arrays located relative to common lattice can compute overlaps, data exchanges, State of system = union of static, dynamic arrays, with functions: constructors, data exchange, time updates Source, receiver data: arbitrary locations, position relative to reference lattice, sampling & i/o Storage ptr Local frame Virt.arr.1 Methods: [IST, TRIP 2008] Stored array " Create/resize subarrays " Output " Etc. Storage ptr Local frame Virt.arr.2 7 June 2012 Open Source E+P Software 6
7 Our Implementation: IWAVE ISO C99 Object oriented C : built around small set of C structs containing data and functions operating on them Core modules: services memory, comm, i/o, job control State repn = RDOM = array of arrays State type = IMODEL struct with RDOM and many virtual sub- RDOMS, functions eg. tsf(rdom * p, int * iv, void * pars)! Application modules ( apps ) choices of physics, scheme Parallelism via domain decomposition, MPI. Reads, writes data in standard exchange formats: initially SEGY/SU, RSF, Open source, X11 license 7 June 2012 Open Source E+P Software 7
8 IWAVE & SEAM Phase I Public domain QC code high accuracy FDTD, ABCs, SEAM-sized data, scale to 1000 s of cores Couldn t find one, so we built it For the details: new SEG e-book by Fehler & Keliher - many insights into project management, QC role of IWAVE 7 June 2012 Open Source E+P Software 8
9 Visual Comparison: Shot 20433, E-W line at N km Tierra 7 June 2012 Open Source E+P Software 9
10 Visual Comparison: Shot 20433, E-W line at N km IWAVE 1 March 2012 HPC in Oil and Gas
11 IWAVE Documentation 7 June 2012 Open Source E+P Software 11
12 Abstract Optimization and Linear Algebra [Rice Vector Library] 7 June 2012 Open Source E+P Software 12
13 Types for Abstract Optimization Essential step: define types for high level abstractions Space, Vector, (linear or nonlinear) Operator, Functional Evaluation objects organize the value of function & derivatives at a point, enforce coherency With these, can express coordinate free algorithms of linear algebra and optimization Krylov (CG etc.), Lanczos, Landweber, quasi-newton, 7 June 2012 Open Source E+P Software 13
14 Our Implementation: the Rice Vector Library ( RVL ) C++ classes expressing calculus in Hilbert Space Design Paper: Padula, Scott & S, ACM TOMS 2009 Standard interfaces to concrete data types in-core, out-ofcore, distributed, - and operations on them: DataContainer data abstraction, forms Visitor pattern with FunctionObject encapsulates all actions on data 7 June 2012 Open Source E+P Software 14
15 Abstract Optimization with RVL Typical use: RTM looks like MyKindaDataSpace dsp( ); MyKindaModelSpace msp( ); Vector m(msp); Vector g(msp); Vector d(dsp); MyKindaModelingOp op(.); OperatorEvaluation opeval(op,m); opeval.getderiv().applyadj(d,g); THE MATH IS THE API! 7 June 2012 Open Source E+P Software 15
16 Abstract Optimization with RVL Built on RVL: Optimization Library UMin: LBFGS, trust region G-N-K, CG, Arnoldi Abstract time-stepping library TSOpt, including universal implementation of optimal checkpointing (Griewank 92) Plans: additional algorithms (L1, TV, TR-SQP, ) 7 June 2012 Open Source E+P Software 16
17 Inversion [RVL + IWAVE = IWAVE++] 7 June 2012 Open Source E+P Software 17
18 Requirements for inversion implementations modeling: forward modeling linearized ( Born ) modeling adjoint (transposed) linearized modeling optimization algorithm, implementation interface between modeling and optimization Natural type mismatch between modeling & optimization concrete (grids, traces) vs. abstract (vectors, operators) Internal state of simulator need not be a Vector object only input and output types 7 June 2012 Open Source E+P Software 18
19 Our Solution: IWAVE++ Middleware layer C++ classes encapsulating input & output types for IWAVE as RVL vector classes out-of-core design Born & adjoint extensions of IWAVE function interfaces, eg. tsfa(rdom * p, RDOM * r, int iv, void * pars) delegates time loop control, checkpointing to TSOpt Defines abstract RVL Operator class combining fwd, lin, and adj modeling [WWS, Enriquez & Sun, Geophys. Prosp. 11] 7 June 2012 Open Source E+P Software 19
20 Our Implementation: IWAVE++ Simple expl adjoint ( dot product ) test IWaveOp<(list of policy types)> op(dom, rng, pars, stream, minit);! Vector<float> m(op.getdomain());! (initialize m)! OperatorEvaluation<float> opeval(op,m);! AdjointTest(opeval.getDeriv(), rnd, stream);! Output, Marmousi 4m grid, 960 cores, 4x1 dom decomp: adjoint relation holds: <Ax,y>-<x,A'y> / Ax y = e-12 < 100*macheps = e-05 <Ax,y> = e+05 <x,a'y> = e+05 Ax y = e+09 7 June 2012 Open Source E+P Software 20
21 Releases and Availability 7 June 2012 Open Source E+P Software 21
22 Releases, plans IWAVE: initial release at SEG 09 initial through current (1.5) at TRIP web site beginning with next release (2.0, 12 Q3) at SourceForge svn rsf.svn.sourceforge.net/svnroot/rsf/trunk download and install either stand-alone, or integrated with Madagascar RVL: initial release 11 Q3 r1.2 coming 12 Q3 IWAVE++: beta Initial release planned for early 13 7 June 2012 Open Source E+P Software 22
23 Thanks to IWAVE team Igor Terentyev, Tanya Vdovina, Xin Wang RVL team Mark Gockenbach, Shannon Scott, Tony Padula, Hala Dajani IWAVE++ team - Dong Sun, Marco Enriquez Max Deschantsreiter, John Anderson, Scott Morton, Christof Stork, Ted Baragy, Murtaza Ali, John Mellor- Crummey, John Washbourne SEAM Project, NSF, sponsors of TRIP 1 March 2012 HPC in Oil and Gas
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