The Coming of Age of Computational
Science
Linda Petzold
Department of Mechanical and Environmental Engineering
Department of Computer Science
University of California Santa Barbara
Outline
• The emerging discipline of computational science
and engineering
• The revolution at the microscale
• Current trends and future directions
Theory, Experiment and
Computation
Growth in the expectations for and applications of CSE
methodology has been fueled by rapid and sustained
advances over the past 30 years of computing power and
algorithm speed and reliability, and the emergence of
software tools for the development and integration of
complex software systems and the visualization of results.
In many areas of science and engineering, the boundary
has been crossed where simulation, or simulation in
combination with experiment is more effective (in some
combination of time/cost/accuracy) than experiment alone
for real needs. In addition, simulation is now a key
technology in industry.
Growth of Capabilities of Hardware and Algorithms
Updated version of chart appearing in “Grand Challenges: High performance computing and
communications”, OSTP committee on physical, mathematical and Engineering Sciences, 1992.
The Revolution at the Microscale
• Behavior near walls and boundaries
is critical
• Large molecules moving through
small spaces
• Interaction with the macroscale world
is still important
The Multiscale World
•Quasicontinuum method (Tadmor,
Ortiz, Phillips, 1996) Links atomistic
and continuum models through the finite
element method. A separate atomistic
structural relaxation calculation is
required for each cell of the FEM mesh
instead of using empirical constitutive
information. Predicts observed
mechanical properties of materials on
the basis of their constituent defects
•Hybrid finite element/molecular
dynamics/quantum mechanics method
(Abraham, Broughton, Bernstein,
Kaxiras, 1999) Massively parallel, but
designed for systems which involve a
central defective region surrounded by a
region which is only slightly perturbed
from equililibrium
Nakano et al.
More Multiscale
•Hybrid finite element/molecular
dynamics/quantum mechanics algorithm
(Nakano, Kalia and Vashista, 1999)
•Adaptive mesh and algorithm
refinement (Garcia, Bell, Crutchfield,
Alder, 1999) Embeds a particle method
(DSMC) within a continuum method at
the finest level of an adaptive mesh
refinement hierarchy – application to
compressible fluid flow
•Coarse stability and bifurcation analysis
using time-steppers (Kevrekidis, Qian,
Theodoropoulos, 2000)
The “patch” method
Nakano et al.
This is only a small sample: There is a new
journal devoted entirely to multiscale issues!
Engineering Meets Biology
Computational Challenges:
•Multiscale simulation
•Understanding and controlling highly nonlinear network behavior
(140 pages to draw a diagram for network behavior of E. Coli)
•Uncertainty in network structure
•Large amounts of uncertain and heterogeneous data
•Identification of feedback behavior
•Simulation, analysis and control of hybrid systems
•Experimental design
Multiscale Simulation of Biochemical Networks
In the heat-shock response
in E. Coli, an estimated 2030 sigma-32 molecules per
cell play a key role in
sensing the folding state of
the cell and in regulating
the production of heat
shock proteins. The system
cannot be simulated at the
fully stochastic level, due to
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•Multiple time scales
(stiffness)
•The presence of
exceedingly large
numbers of molecules
that must be accounted
for in SSA
Khammash et al.
Beyond Simulation: Computational Analysis
•Sensitivity analysis
•Forward and adjoint methods – ODE/DAE/PDE; hybrid systems
Multiscale, stochastic,… still to come
•Uncertainty analysis
•Polynomial chaos, deterministic systems with uncertain
coefficients
•Many other ideas – special issue in progress, SIAM SISC
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•Design optimization/optimal control
•Design of experiments – to what extent can you learn something
from incomplete information?, where is the most predictive power?
More Computational Analysis
•Determination of nonlinear structure – multiscale, stochastic, hybrid
•Bifurcation
•Mixing
•Long-time behavior
•Invariant manifolds
•Chaos
•Control mechanisms – identifying feedback mechanisms
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•Reduced/simplified models – deterministic, multiscale, stochastic,
hybrid systems, identify the underlying structure and mechanism
•Data analysis – revealing the interconnectedness, dealing with
complications due to data uncertainties
Computer Science will Play a Much Larger Role
Pragmatic reasons: Significant help from software tools
•Source-code generation
•Automatic differentiation – enables greater accuracy and
reliability (and saves work in writing derivative routines and
especially in debugging!) in generation of Jacobian matrix
•Fix the dumb things we have done in codes , like ‘if’
statements in functions that are supposed to be continuous
•Thread-safety - identify and fix the problems so that the

code is ready for parallel/grid computing
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•User interfaces: by current standards in the
rest of the computer world, user interfaces for
scientific computing look like this:
Some exceptions and coming developments:
•Matlab
•Semi-automatic generation of GUI
(MAUI,JMPL), for big production codes and
dusty decks
•Component technologies (PETSC)
Computer Science will Play a Much Larger Role
The deeper reason:
At the smaller scales, we are dealing with and manipulating large
amounts of discrete, stochastic, Bayesian, Boolean information.
These are the foundations of Computer Science. Bioinformatics is
just the tip of the iceberg.
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