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UID:2f9acaa5f98c1f4e6c6592c790e1ef05
CATEGORIES:Colloquia
CREATED:20260127T115046
SUMMARY:Structure preserving scientific machine learning through discrete exterior calculus
LOCATION:Hill 705
DESCRIPTION:While AI and machine learning continue to make rapid progress, the ad hoc c
 onstruction of model architectures presents major challenges for developing
  scientific machine learning methods that preserve the theoretical guarante
 es underpinning conventional modeling and simulation. In this talk, we pres
 ent recent work developing hybrid transformer–finite element architectures 
 that incorporate the design principles of finite element exterior calculus 
 (FEEC). Using this framework, we formulate equality-constrained optimizatio
 n problems that allow us to reverse engineer reduced-order descriptions of 
 physical systems from data while preserving topological structure. We provi
 de an overview of several results based on this approach: mixed finite elem
 ent methods yield autoregressive models that outperform foundation models w
 ith 1000× fewer parameters; metriplectic brackets preserve nonequilibrium s
 tatistics in coarse-grained systems; and coordinate-free representations of
  geometry and physics produce models that remain accurate on geometries uns
 een during training.\n
X-ALT-DESC;FMTTYPE=text/html:<p>While AI and machine learning continue to make rapid progress, the ad ho
 c construction of model architectures presents major challenges for develop
 ing scientific machine learning methods that preserve the theoretical guara
 ntees underpinning conventional modeling and simulation. In this talk, we p
 resent recent work developing hybrid transformer–finite element architectur
 es that incorporate the design principles of finite element exterior calcul
 us (FEEC). Using this framework, we formulate equality-constrained optimiza
 tion problems that allow us to reverse engineer reduced-order descriptions 
 of physical systems from data while preserving topological structure. We pr
 ovide an overview of several results based on this approach: mixed finite e
 lement methods yield autoregressive models that outperform foundation model
 s with 1000× fewer parameters; metriplectic brackets preserve nonequilibriu
 m statistics in coarse-grained systems; and coordinate-free representations
  of geometry and physics produce models that remain accurate on geometries 
 unseen during training.</p>
CONTACT:Nat Trask
DTSTAMP:20260827T051730
DTSTART;TZID=America/New_York:20260313T153000
DTEND;TZID=America/New_York:20260313T163000
SEQUENCE:0
TRANSP:OPAQUE
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