Enhancing Experimental Design and Understanding with Deep - PowerPoint PPT Presentation

Enhancing Experimental Design and Understanding with Deep Learning/AI Vic Castillo, Ph. D. Computational Engineering Lawrence Livermore National Laboratory March 28, 2018 LLNL-PRES-748201 This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE- AC52-07NA27344. Lawrence Livermore National Security, LLC

Enhancing Experimental Design • Complex Systems such as manufacturing process, energy systems, fusion reactors have a large design space. • Intelligent sampling / Experimental design can help. • Simulation, like experiments, can be expensive. • DNN’s can make good, fast -running surrogate models. Main Idea: Leverage ML and GPUs to help the designer navigate a complex design space at rapid cadence by giving quicker feedback. This leads to more agile development and enhances creativity. LLNL-PRES-748201

Example Application: Glass production LLNL-PRES-748201

Generating the f fast- runnin ing flo low vis isualizer • Deep Convolutional autoencoder used to reduce simulation state space to a reduced latent space • Fully-connected neural network to correlate control and design parameters to latent space • Projection to full state space is from the decoder LLNL-PRES-748201

Parameter Space Sampling This is a review of a framework for developing and evaluating speculative sampling methods. Classical statistical sampling is used as a baseline and incorporated. A simple coupled oscillator model with a six-dimensional design space is used as a prototype. A recent development from Google Deep Mind is discussed. Example runs are used for discussion. LLNL-PRES-748201

Sim imple Example: Coupled Oscil illa lator Design Parameters: • Two masses {m 1 , m 2 } • Connected with a damping spring {k 12 , c 12 } • Tethered to the origin with damping springs {k 1 , c 1 , k 2 , c 2 } • Subject to a time-dependent body force {F 1 , F 2 , t 1 , t 2 , t 3 } Coupled Oscillator State Space: 𝑦 1 , ሶ 𝑦 2 }(t) {x 1 , x 2 , ሶ Simple, explainable system with a reasonably- complex Design Space: {m 1 , m 2 , k 1 , c 1 , k 2 , c 2 , k 12 , c 12 , F 1 , F 2 , t 1 , t 2 , t 3 } LLNL-PRES-748201

Parameter Space Let’s consider 6 parameters to vary in our design space: {c 1 , c 12 , c 2 , k 1 , k 12 , k 2 } In a “coded” space, each parameter can be varied from -1 to +1. A scale can be assigned to describe regions Scaled regions are at centers and extremes: p i ~ {-1, 0, +1} In the figure, p i ∈ 0 +/- 0.05, ∀ i LLNL-PRES-748201

Mapping parameter space For convenience, we map test regions that span a 6D hypercube to a 2D grid (3 3 x3 3 ) Each region has a scale Regions span the space but may not completely cover it \01 Mapping Parameter Space LLNL-PRES-748201

Box-Behnken (1960) Classic Statistical Sampling provides a baseline Guarantees a smooth quadratic fit in high- dimensional space D samples Designs are rotatable 3 12+center 6D -> 720 permutations 4 24+center 5 40+center 6 48+center 7 56+center 8 112+center 9 96+center 10 160+center 11 176+center 12 192+center \02 BoxBehnken 16 384+center LLNL-PRES-748201

Learning the Transition Function A Neural Network is used to learn the transition function: Design Parameters: {c 1 , c 12 , c 2 , k 1 , k 12 , k 2 } + Body Force: F(F 1 ,F 2 ,t) 𝑦 1 , ሶ 𝑦 2 }(t) + State: {x 1 , x 2 , ሶ → NewState: {x 1 , x 2 , ሶ 𝑦 1 , ሶ 𝑦 2 }(t+ ∆ t) Learned Dynamics \03 Learning Transition Function LLNL-PRES-748201

Predic iction Error System was trained from region {0,0,0,0,0,0} with a scale of 0.10 Prediction is done in region {-1,0,0,0,0,0} with a scale of 0.01 Predictor has not seen this dynamic, but tries! Error is calculated as the integrated L1 norm: Extrapolated Dynamics 𝑢 𝑔 𝑄𝑠𝑓𝑒 𝑢 − 𝐷𝑏𝑚𝑑(𝑢) Error = ׬ 𝑢 0 LLNL-PRES-748201

Mapping predic iction error Error for each region is mapped to grid for each state component Patterns can reveal parameter interactions Error is calculated as the integrated L1 norm: 𝑢 𝑔 𝑄𝑠𝑓𝑒 𝑢 − 𝐷𝑏𝑚𝑑(𝑢) Error = ׬ 𝑢 0 LLNL-PRES-748201

Population-based Training New method by Google Deep Mind (28 November 2017) Used to search out optimal hyper- parameters for DNNs Can be used as a sampling method Leverages Explore vs. Exploit LLNL-PRES-748201

Exp xperiment: Agent-based Sampli ling Six agents explore center region {0,0,0,0,0,0} with scale = 0.10 State transitions are stored in DB Random transitions are used to train Prediction 0 Local Error in all regions is calculated Agents move to a random Box-Behnken region (scale = 0.10) and explore Initial local error is calculated (current prediction) Agents with low error move to help others Simulations continue LLNL-PRES-748201

Exp xperiment: Agent-based Sampli ling Six agents explore center region {0,0,0,0,0,0} with scale = 0.10 State transitions are stored in DB Random transitions are used to train Prediction 0 Local Error in all regions is calculated Agents move to a random Box-Behnken region (scale = 0.10) and explore Initial local error is calculated (current prediction) Agents with low error move to help others Simulations continue LLNL-PRES-748201

Exp xperiment: Agent-based Sampli ling Six agents explore center region {0,0,0,0,0,0} with scale = 0.10 State transitions are stored in DB Random transitions are used to train Prediction 0 Local Error in all regions is calculated Agents move to a random Box-Behnken region (scale = 0.10) and explore Initial local error is calculated (current prediction) Agents with low error move to help others Simulations continue LLNL-PRES-748201

Specula lativ ive Sampling LLNL-PRES-748201

Simple Sampling Speculative Sampling Round 0 Sampling Center Region LLNL-PRES-748201

Simple Sampling Speculative Sampling Round 1 Sampling 7/729 Regions LLNL-PRES-748201

Simple Sampling Speculative Sampling Round 2 Sampling 13/729 Regions LLNL-PRES-748201

Simple Sampling Speculative Sampling Round 3 Sampling 19/729 Regions LLNL-PRES-748201

Simple Sampling Speculative Sampling Round 4 Sampling 25/729 Regions LLNL-PRES-748201

Simple Sampling Speculative Sampling Round 5 Sampling 31/729 Regions LLNL-PRES-748201

Simple Sampling Speculative Sampling Round 6 Sampling 37/729 Regions LLNL-PRES-748201

Simple Sampling Speculative Sampling Round 7 Sampling 43/729 Regions LLNL-PRES-748201

Simple Sampling Speculative Sampling Round 8 Sampling 49/729 Regions LLNL-PRES-748201

TensorFlow im imple lementation TensorFlow can be used for the solver Allows hardware control: Solver/Simulator -> CPU Learning -> GPU Inference -> TPU/neuromorphic Allows algorithm instrumentation LLNL-PRES-748201

Discussion • Simple system for prototyping – Coupled Oscillator • Small parameter space – {c 1 , c 12 , c 2 , k 1 , k 12 , k 2 } • Mapping parameter space to 2D grid • Classical sampling baseline – Box-Behnken • Learning the transition function • Mapping prediction error • Population-based search • Experiments • TensorFlow implementation LLNL-PRES-748201