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t 5. t 4. t 3. t 2. t 1. time. Physics-Based Constraints in the Forward Modeling Analysis of Time-Correlated Image Data. James L. Carroll and Christopher D. Tomkins. LANL P-21.

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Physics-Based Constraints in the Forward Modeling Analysis of Time-Correlated Image Data

James L. Carroll and Christopher D. Tomkins


  • We tested 1 through 5 degrees of temporal freedom, and 8 different noise levels, resulting in a 5X8 matrix of experiments, each tested with 12 different numbers of optimization steps (up to 300,000), for both an independent forward modeling analysis, and a dynamic time series analysis, each averaged over 100 independent runs.

Time Series Constraints


We study the application of physics based constraints on the forward modeling analysis of hydrodynamic explosive data. These constraints impose a temporal regularization, restricting the space of potential reconstructions to the space of physically realizable solutions, thus improving the quality of density reconstructions produced. We study the potential applicability of this approach to experiments at Los Alamos National Laboratory’s DARHT facility with simulated data.

  • The forward-modeling framework makes possible a global optimization procedure

Now, physics-based constraints on the evolution of the

time-series data will also constrain the (global) solution

Prior knowledge provides additional

constraints at each time







SOLUTION:Evaluated Density




  • High Explosives (HE) driven experiments to study material properties under intense pressures and high velocities.
  • Radiographs of chosen instants during dynamic conditions.
  • Metals and other materials may flow like liquids under the high temperatures and pressures produced by HE.
  • The principle challenge is to summarize this vast body of data in order to draw meaningful conclusions. Each experiment in the 5X8

Data constrain solution at each time





  • array resulted in a graph like the one shown on the right. From this matrix of results, we extracted the following summary information:
  • These physics-based constraints will maximize information extracted from each dataset

Concept: Can we learn something about the solution at time 3 (blue) from the data at surrounding times?

Approach: use physics to constrain solution at each time based upon time-series of data.


When certain conditions are met:

  • 1) Must have the time between measurements (Dt) on the order of a relevant time scale of the flow; and

2) Must have non-perfect data (due to noise, background levels, etc).

Consider an evolving interface:

Static Cylinder Set-up

Static Cylinder shot

Static Cylinder Radiograph

  • Final Model Error
  • Advantage (the difference between the time series approach and the independent analysis approach)
  • The number of optimization steps before the optimization subjectively “converged”
  • The noise level where optimization harmed the solution instead of improving it (the “overfit point”).
  • This summary information is presented in the following graphs:

Firing Point


Phase 2: “Second Axis”

Lab Space and Control Rooms

Optics and Detector Bunker

Data must be correlated in time

Perfect data might render the information in the time series un-necessary, while noisierdata should add value to global optimization.

Phase 1: “First Axis”

Slide 1

DARHT is the USA’s premiere hydrodynamics testing facility, providing two intense energy radiographic views of explosives driven dynamic

Final Error


Physics Model: Radius Evolving through Time

experiments. Axis 2, which was completed in 2009, has the capability of producing and imaging four distinct pulses. This provides a view of the dynamics of the experiments through time. The purpose of our research is to explore potential analysis techniques to make better use of this temporal time series information.

Signal To Noise Ratio

  • Degrees of Temporal Freedom:
    • 1:
    • 2:
    • 3:
    • 4:
    • n:

Forward Modeling Image Analysis


Signal to Noise Ratio


Simulated Radiographs:

  • For all degrees of freedom:
    • Time series advantage first grows as the signal to noise level drops, then falls in extreme noise
  • Time series analysis acts as regularization, and delays the onset of overfit as noise is added
    • This regularization can involve the imposition of physics based constraints on the space of acceptable solutoins
  • Time series analysis provides improvement even when the problem is underconstrained
  • Time series analysis involves a more complex optimization problem than does static analysis, converging more slowly

Time Step 1

Time Step 2

Time Step 3

Time Step 4

True Densities:

Unobserved Starting Position

Time Step 1

Time Step 2

Time Step 3

Time Step 4

Signal To Noise Levels Tested:

The forward modeling analysis approach (sometimes called “analysis by synthesis”) involves optimizing the parameters of a model, in order to minimize the differences between a synthetic radiograph and the actual data. Essentially, it solves a computer vision problem through the application of computer graphics and function optimization. This approach has been shown to perform well, especially under the highly constrained conditions commonly found in scientific imaging experiments.

This work is supported by The Advanced Radiography Science Campaign (C3), PM E. Mullen.