Dr. Steven G. Wax, Director Dr. Brett P. Giroir, Deputy Director Dr
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Dr. Steven G. Wax, Director Dr. Brett P. Giroir, Deputy Director Dr. Carey Schwartz, Program Manager Applied and Computational Mathematics Program DARPA’s Mission DARPA’s mission is to prevent technological surprise from harming our national security by sponsoring revolutionary, high-payoff research that bridges the gap between fundamental discoveries and their military use DARPA Accomplishments 19601960 UCAV Global Hawk Saturn Vela Hotel 19701970 Ground TMR MEMS Surveillance Radar ATACMS 20002000 JSF MALD M-16 Rifle JSTARS 19801980 Uncooled IR Stealth Fighter Arpanet 19901990 BAT Sea Shadow GPS Taurus Launch Predator Vehicle DARPA Organization Director, Tony Tether Deputy Director, Bob Leheny Information Exploitation Tactical Technology Special Projects Advanced Technology Ted Bially Art Morrish Amy Alving Dave Honey Robert Popp/Robert Tenney Gary Graham/Stephen Welby Joe Guerci Larry Stotts Air/Space/Land Platforms Chem/Bio Def Systems Sensors Unmanned Systems Counter Underground Assured C3ISR Facilities Space Operations Exploitation Systems Space Maritime Laser Systems Sensors/Structures Command & Control Early Entry/Special Future Combat Systems Navigation/Sensors/ Forces Planning / Logistics Signal Processing Information Processing Joint Unmanned Defense Sciences MicrosystemsTechnology Steven Wax Technology Combat Air Systems Ron Brachman Zach Lemnios Mike Francis Brett Giroir Barbara Yoon John Zolper Bio Warfare Cognitive Systems Electronics Common Systems & Defense Computational - Optoelectronics Technologies Technologies Perception MEMS X-45 System Biology Representation & X-47 System Materials & Reasoning Combined Devices Microsystems Mathematics Learning Natural Communication APPROVED FOR PUBLIC RELEASE 39873 DARPADARPA Strategic VisionVision • Strategic Thrusts • Precision detection, tracking, and destruction of elusive surface targets • Characterization of underground structures • Force multipliers for urban combat • Networked manned & unmanned attack operations • Assured use of space Maintain the technological • Cognitive systems Maintain the technological superioritysuperiority of of the the U.S. U.S. • Bio-Revolution militarymilitary and and prevent prevent • Robust, secure self-forming networks technologicaltechnological surprise surprise … … • Enduring Foundations High-payoffHigh-payoff research research that that • Materials bridgesbridges the the gap gap between between • Microsystems fundamentalfundamental discoveries discoveries andand their their military military use. use. • Information Technologies Defense Sciences Office Exploit discoveries and innovations Paradigm shifts in defense in science and engineering capabilities Mine the “Far Side of the Breakthroughs to Exploit Far Side” Biological Sciences Materials & Devices Mathematics Diverse Disciplines Diverse Programs Engineering, Physics, Materials, Nanoscale Mathematics Structures Medicine, Microbiology, Hardware/Devices Biochemistry in the hands of soldiers DSO vs. others • “The flying machine • “We started assembly which will really fly might today” be evolved by the combined and – Orville Wright’s Diary continuous efforts of • 9 October 1903 mathematicians and mechanicians in from one million to ten million years” –The New York Times • 9 October 1903 DSO – Technical Personnel Dr.Dr. Steven Steven G. G. Wax, Wax, Dir Dir Dr.Dr. Brett Brett P. P. Giroir, Giroir, Dep Dep Dir Dir Dr.Dr. Joseph Joseph Bielitzki Bielitzki Dr.Dr. Valerie Valerie Browning Browning Dr.Dr. Geoff Geoff Ling Ling (LTC (LTC (p), (p), USA) USA) Dr.Dr. Leonard Leonard Buckley Buckley Dr.Dr. John John Lowell Lowell (Maj, (Maj, USAF) USAF) Dr.Dr. Ralph Ralph Chatham Chatham Dr.Dr. John John Main Main Dr.Dr. Leo Leo Christodoulou Christodoulou Dr.Dr. Ben Ben Mann Mann Dr.Dr. William William Coblenz Coblenz Dr.Dr. Rick Rick Satava Satava Dr.Dr. Douglas Douglas Cochran Cochran Dr.Dr. Carey Carey Schwartz Schwartz Dr.Dr. Mildred Mildred Donlon Donlon Dr.Dr. Morley Morley Stone Stone Dr.Dr. Eric Eric Eisenstadt Eisenstadt Dr.Dr. Terrence Terrence Weisshaar Weisshaar Dr.Dr. Anantha Anantha Krishnan Krishnan Dr.Dr. Stuart Stuart Wolf Wolf DSO Office Thrusts Materials Mathematics Biological & Devices Sciences Structural Materials and Applied Mathematics Biological Warfare Defense Components Smart Materials and Basic Research in Maintain Human Performance Structures Mathematics Functional Materials Enhanced System Performance Power and Water Bio-Materials TheThe ParadoxParadox ofof MathematicsMathematics • Users of mathematics think that all the mathematics necessary for progress already exists and that practitioners already have sufficient mathematical skills with these tools to proceed. – Therefore, we don’t need mathematicians and can concentrate on scientific and technological problems at hand. • Mathematicians feel that applications are secondary and practitioners really don’t understand why mathematics is important or how to use it. – Therefore we don’t need practitioners and can concentrate on inventing new mathematics. • Thus both groups feel, since the other is clearly self- serving and misguided, that they can safely ignore each other. MathematicsMathematics at at DARPA: DARPA: Focused Focused effort effort that that both both incorporates incorporates existingexisting mathematics mathematics and and develops develops ne neww mathematics mathematics to to be be used used at at criticalcritical points points in in the the solutions solutions of of many many DARPA-hard DARPA-hard DoD DoD problems. problems. Exploiting Mathematics DecreasingDecreasing TimeframeTimeframe OfOf OperationsOperations OnOn TheThe BattlefieldBattlefield IsIs AtAt OddsOdds WithWith TheThe TrendTrend TowardsTowards AnAn IncreasinglyIncreasingly ComplexComplex BattlefieldBattlefield Environment.Environment. OverOver 50%50% OfOf GainsGains InIn SpeedSpeed HaveHave BeenBeen DueDue ToTo MathematicsMathematics (Improved(Improved Algorithms)Algorithms) NotNot Moore’sMoore’s LawLaw (Computer(Computer Speed).Speed). • Determining Representations -- Optimizing Dimensionality! • Representation and Analysis of Large and/or Disparate Data Sets • Adaptive Sensors and Waveforms • Modeling of Materials, Physics and Biology • Quantifying and Bounding Uncertainty and Robustness The 21st Century Battlespace Advanced Computational Math Virtual Electromagnetic Testrange Integrated Sensing & Refine new mathematical Processing developments and bring them to Physical Field practice in design of LO air (continuum) vehicles Numerical analysis (fast multipole PHYSICAL method) LAYER Computational geometry Establish a consortium of major PROCESSING LAYER airframers Symbolic Output EXPLOITATION ISP closes the sensing system loop system sensing LAYER • Globally optimized sensor system designs allow the integration of independently optimized sensor components PerformancePerformance GraphsGraphs Exploiting Complex Systems Method of Moments (MOM) Fast Multipole Method (FMM) # flops # flops 14 ++ 18 10 • 10 4 Full Vehicles Full Vehicles 12 13 10 • 10 O(N^2) 3 O(N log N) Components Components 12 12 10 10 Details Details 10K 25K 1,000K+ 10K 25K 1,000K+ N = # unknowns N = # unknowns PredictingPredicting MaterialMaterial PropertiesProperties Property of interest and Goal Materials of Interest • Nonlinear optical materials Theoretical description • Diluted magnetic semiconductors •Macroscopic • Mesoscopic • Thermoelectrics •Microscopic • Ferroelectrics my, mx depend on the electronic structure • High energy density materials Ab initio electronic structure calculations Ab initio electronic structure calculations for many structures and compositions for many structures and compositions Direct Inverse Method MultiscaleMultiscale methods methods SearchSearch Algorithms Algorithms errors errors Optimized material Optimized material errors Experimental Experimental validation validation TimeTime ReversalReversal Propagation Exploit multiple scattering for Single Scattering Event Path medium image formation and a communication e a Two Scattering All paths other than the direct path Event Path AB from A to B through the propagation Direct Path medium is multipath Multiple scattering can increase the effective aperture from a to ae. Multiple Scattering Event Path Testbeds Image Formation and Antennas Target Signature Propagation HumanHuman AssistedAssisted NeuralNeural DevicesDevices UseUse brainbrain activityactivity toto directlydirectly controlcontrol prostheticsprosthetics andand peripheralperipheral devicesdevices • Progress – Open loop, brain control of “prosthetic” arm – Beginning demonstration in human subjects – Coordinating with VA – Begin correlating to non-invasive electric (EEG) or magnetic (MEG) fields Geo*Geo* ---- AddressinAddressingg GeometricGeometric ShortfallsShortfalls • New Representations for Surface and Geodetic Data – 100X improvement in storage with no loss of precision in end application – Easily Conflated/Deflated (30-60 Hz) for images, 1 Hz for gravity • Automated Registration – Tactical Imagery (256 x 256) to Digital Point Precision Data Base at 30 HZ (500 x improvement – Contrast, Illumination, and Scale, Invariant Methods Representations • Error Management – Multiresolution representation that supports multiple applications with a variety of accuracy requirements Topological Data Analysis RECOGNIZE THE PLAYING FIELD BEFORE THE GAME STARTS • Discovery of the shape of a data set is the necessary first step toward finding high value targets. • It is striking that this fundamental question has been ignored in