<\/p>\n\n\n\n
Presented by: Dr. Nat Trask<\/strong><\/p>\n\n\n\n University of Pennsylvania<\/strong><\/p>\n\n\n\n Hosted by:<\/p>\n\n\n\n Mathematics in Computation Talk Series<\/strong><\/p>\n\n\n\n <\/p>\n\n\n\n Abstract: <\/strong><\/p>\n\n\n\n Within the last year, the artificial intellI community has turned a renewed focus toward engineering and physical sciences, both within the U.S. Department of Energy (DOE) and industry. Many of these efforts hinge upon an assumption that scale alone will be able to achieve predictive scientific models. To date, however, works show that neural physics models rapidly degrade as they are used at the periphery of their training data distribution; this presents a major risk to applying them to design or discovery tasks which, by definition, aim to operate specifically at this frontier. This talk will present recent work in which topological structure in both the representation of geometry and of physics can be used to construct models that are able to extrapolate: both in the sense of predicting physics on geometries or forecasting to future times unseen during training. This structure can be accessed by developing hybrid neural architectures which wrap state-of-the-art transformers in a \u201ctopological scaffold\u201d provided by mixed finite element machinery. By exposing variational structure, provable properties are established regarding stability and accuracy for learned models which is intractable for contemporary \u201cblack-box\u201d architectures. Several examples from both community benchmarks and DOE digital twinning efforts are provided where these architectures are able to achieve state of the art performance, often with orders of magnitude smaller models.<\/p>\n\n\n\n Speaker\u2019s Bio:<\/strong><\/p>\n\n\n\n Dr. Trask is an associate professor in the Mechanical Engineering and Applied Mechanics department at the University of Pennsylvania. He maintains a joint appointment with Sandia National Laboratories, and is co-director of Scalable, Efficient and Accelerated Causal Reasoning Operators, Graphs and Spikes for Earth and Embedded Systems, a DOE Mathematical Multifaceted Integrated Capability Center developing next generation scientific machine learning architectures. He has worked on a number of application areas spanning multi-scale\/multi-physics in fluids, solids, electromagnetism, materials, and solid-state physics. <\/strong><\/p>\n\n\n\n Host<\/strong>: <\/p>\n\n\n\n Viktor Reshniak,\u00a0reshniakv@ornl.gov<\/a>,\u00a0865-341-4394<\/p>\n","protected":false},"excerpt":{"rendered":" Presented by: Dr. Nat Trask University of Pennsylvania Hosted by: Mathematics in Computation Talk Series Abstract: Within the last year, the artificial intellI community has turned a renewed focus toward engineering and physical sciences, both within the U.S. Department of Energy (DOE) and industry. Many of these efforts hinge upon an assumption that scale alone<\/p>\n","protected":false},"author":110,"featured_media":585,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-889","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized"],"acf":[],"_links":{"self":[{"href":"https:\/\/events.ornl.gov\/mictalks\/wp-json\/wp\/v2\/posts\/889","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/events.ornl.gov\/mictalks\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/events.ornl.gov\/mictalks\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/events.ornl.gov\/mictalks\/wp-json\/wp\/v2\/users\/110"}],"replies":[{"embeddable":true,"href":"https:\/\/events.ornl.gov\/mictalks\/wp-json\/wp\/v2\/comments?post=889"}],"version-history":[{"count":1,"href":"https:\/\/events.ornl.gov\/mictalks\/wp-json\/wp\/v2\/posts\/889\/revisions"}],"predecessor-version":[{"id":890,"href":"https:\/\/events.ornl.gov\/mictalks\/wp-json\/wp\/v2\/posts\/889\/revisions\/890"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/events.ornl.gov\/mictalks\/wp-json\/wp\/v2\/media\/585"}],"wp:attachment":[{"href":"https:\/\/events.ornl.gov\/mictalks\/wp-json\/wp\/v2\/media?parent=889"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/events.ornl.gov\/mictalks\/wp-json\/wp\/v2\/categories?post=889"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/events.ornl.gov\/mictalks\/wp-json\/wp\/v2\/tags?post=889"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}},{"id":567,"date":"2026-09-25T10:01:00","date_gmt":"2026-09-25T14:01:00","guid":{"rendered":"https:\/\/events.ornl.gov\/mictalks\/?p=567"},"modified":"2026-10-08T16:38:37","modified_gmt":"2026-10-08T20:38:37","slug":"fast-high-dimensional-kronecker-tensor-operations-for-sparse-grids","status":"publish","type":"post","link":"https:\/\/events.ornl.gov\/mictalks\/fast-high-dimensional-kronecker-tensor-operations-for-sparse-grids\/","title":{"rendered":"Fast High-Dimensional Kronecker Tensor Operations for Sparse Grids"},"content":{"rendered":"\n Abstract:<\/strong><\/p>\n\n\n\n Sparse Grids (SG) is a common tool for applications that require multidimensional function approximation, such as constructing surrogate models in parameter space or solving high-dimensional partial differential equations. From uncertainty quantification to Kinetic models for plasma physics, the key advantage of SG is the mitigation of the computational cost associated with high-dimensional problems, also known as the curse of dimesionality. The grids are constructed from hierarchical superposition of multidimensional tensors of single dimensional basis functions, and the resulting complex structure allows for fine tuning and adapting to the behavior of a specific function with minimal number of degrees of freedom. The linear algebra operations associated with SG resemble algebraic operations using classical Kronecker matrices and Kronecker theory is in turn a powerful tool for tensor linear algebra. The Kronecker structure allows combinations of like-terms and reduction of the overall computational cost by a factor exponential in the number of dimensions. However, the same like-term relationship is lost in a general sparse context.<\/p>\n\n\n\n Several sufficient conditions are presented that enable recovery of the Kronecker cost reduction in a hierarchical sparse-grid context. The analysis considers hierarchy completeness, the direction of information transfer (upward or downward through the hierarchy), and minimal padding strategies. Numerical results demonstrate speedups of up to 100\u00d7, even for moderate dimensions, when computing surplus coefficients for sparse-grid interpolation. Greater speedups are obtained when sparse grids are combined with the Discontinuous Galerkin (DG) method for the solution of high-dimensional Partial Differential Equations (PDEs).<\/p>\n\n\n\n Speaker\u2019s Bio:<\/strong><\/p>\n\n\n\n Dr. Miroslav Stoyanov obtained his Ph.D. in Mathematics from Virginia Tech in 2009. After a postdoctoral assignment at Florida State University, Dr. Stoyanov joined Oak Ridge National Laboratory in 2012, where he has continued his research. His research interests include uncertainty quantification, high-dimensional approximation theory and high-performance computing and the development of mathematical libraries.<\/p>\n\n\n\n <\/p>\n\n\n\n Host<\/strong>:<\/p>\n\n\n\n Pablo Seleson, selesonpd@ornl.gov<\/a>, 865-323-2859 <\/p>\n\n\n\n <\/p>\n","protected":false},"excerpt":{"rendered":" Dr. Miroslav Stoyanov, ORNL Abstract: Sparse Grids (SG) is a common tool for applications that require multidimensional function approximation, such as constructing surrogate models in parameter space or solving high-dimensional partial differential equations. From uncertainty quantification to Kinetic models for plasma physics, the key advantage of SG is the mitigation of the computational cost associated<\/p>\n","protected":false},"author":110,"featured_media":565,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-567","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized"],"acf":[],"_links":{"self":[{"href":"https:\/\/events.ornl.gov\/mictalks\/wp-json\/wp\/v2\/posts\/567","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/events.ornl.gov\/mictalks\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/events.ornl.gov\/mictalks\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/events.ornl.gov\/mictalks\/wp-json\/wp\/v2\/users\/110"}],"replies":[{"embeddable":true,"href":"https:\/\/events.ornl.gov\/mictalks\/wp-json\/wp\/v2\/comments?post=567"}],"version-history":[{"count":2,"href":"https:\/\/events.ornl.gov\/mictalks\/wp-json\/wp\/v2\/posts\/567\/revisions"}],"predecessor-version":[{"id":1066,"href":"https:\/\/events.ornl.gov\/mictalks\/wp-json\/wp\/v2\/posts\/567\/revisions\/1066"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/events.ornl.gov\/mictalks\/wp-json\/wp\/v2\/media\/565"}],"wp:attachment":[{"href":"https:\/\/events.ornl.gov\/mictalks\/wp-json\/wp\/v2\/media?parent=567"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/events.ornl.gov\/mictalks\/wp-json\/wp\/v2\/categories?post=567"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/events.ornl.gov\/mictalks\/wp-json\/wp\/v2\/tags?post=567"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}},{"id":560,"date":"2026-09-22T13:22:49","date_gmt":"2026-09-22T17:22:49","guid":{"rendered":"https:\/\/events.ornl.gov\/mictalks\/?p=560"},"modified":"2026-10-08T16:39:18","modified_gmt":"2026-10-08T20:39:18","slug":"closed-form-logical-error-rate-approximations-for-surface-codes","status":"publish","type":"post","link":"https:\/\/events.ornl.gov\/mictalks\/closed-form-logical-error-rate-approximations-for-surface-codes\/","title":{"rendered":"Closed Form Logical Error Rate Approximations for Surface Codes"},"content":{"rendered":"\n Abstract:<\/strong><\/p>\n\n\n\n The authors propose a novel method to calculate logical error rates in surface codes, assuming independent and identically distributed physical errors. These results fit well known scaling laws for studied physical error rates and code distances but break down in some other regimes. They show how to use their method to analyze hypothetical quantum computers with various configurations and select designs with lower error rates. Currently, this requires expensive classical simulations of quantum decoders for various distances and physical error rates or inaccurate extrapolation from minimal experimental data. Instead, they use the symmetry of the problem to count the configurations that result in a logical error with their novel software. Given a physical error rate, the method can deduce the probability of a logical error to provably good accuracy. The authors include an analysis of measurement errors to allow for a more complete comparison of different surface code implementations. They extend this counting method to a particular locally correlated error model. <\/p>\n\n\n\n Speaker\u2019s Bio:<\/strong><\/strong><\/p>\n\n\n\n Dr. Shaked Regev is a Research Scientist at Oak Ridge National Laboratory whose research interests include Quantum Error Correction, Numerical Linear Algebra, Mathematical Optimization, GPU Programming, and High-Performance Computing. He received his Ph.D. in Computational and Mathematical Engineering from Stanford University for his thesis on “Preconditioning Techniques for Sparse Linear Systems.<\/strong>“<\/p>\n\n\n\n Host<\/strong>:<\/p>\n\n\n\n Elaine Wong, wongey@ornl.gov<\/a>, 865-341-2325<\/p>\n\n\n\n <\/p>\n","protected":false},"excerpt":{"rendered":" Dr. Shaked Regev, ORNL Abstract: The authors propose a novel method to calculate logical error rates in surface codes, assuming independent and identically distributed physical errors. These results fit well known scaling laws for studied physical error rates and code distances but break down in some other regimes. They show how to use their method<\/p>\n","protected":false},"author":110,"featured_media":498,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-560","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized"],"acf":[],"_links":{"self":[{"href":"https:\/\/events.ornl.gov\/mictalks\/wp-json\/wp\/v2\/posts\/560","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/events.ornl.gov\/mictalks\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/events.ornl.gov\/mictalks\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/events.ornl.gov\/mictalks\/wp-json\/wp\/v2\/users\/110"}],"replies":[{"embeddable":true,"href":"https:\/\/events.ornl.gov\/mictalks\/wp-json\/wp\/v2\/comments?post=560"}],"version-history":[{"count":2,"href":"https:\/\/events.ornl.gov\/mictalks\/wp-json\/wp\/v2\/posts\/560\/revisions"}],"predecessor-version":[{"id":1067,"href":"https:\/\/events.ornl.gov\/mictalks\/wp-json\/wp\/v2\/posts\/560\/revisions\/1067"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/events.ornl.gov\/mictalks\/wp-json\/wp\/v2\/media\/498"}],"wp:attachment":[{"href":"https:\/\/events.ornl.gov\/mictalks\/wp-json\/wp\/v2\/media?parent=560"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/events.ornl.gov\/mictalks\/wp-json\/wp\/v2\/categories?post=560"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/events.ornl.gov\/mictalks\/wp-json\/wp\/v2\/tags?post=560"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}},{"id":562,"date":"2026-09-17T15:15:00","date_gmt":"2026-09-17T19:15:00","guid":{"rendered":"https:\/\/events.ornl.gov\/mictalks\/?p=562"},"modified":"2026-10-08T16:39:55","modified_gmt":"2026-10-08T20:39:55","slug":"adaptive-sparse-grid-discontinuous-galerkin-approximations-to-the-bhatnagar-gross-krook-model","status":"publish","type":"post","link":"https:\/\/events.ornl.gov\/mictalks\/adaptive-sparse-grid-discontinuous-galerkin-approximations-to-the-bhatnagar-gross-krook-model\/","title":{"rendered":"Adaptive Sparse-Grid Discontinuous Galerkin Approximations to the Bhatnagar\u2013Gross\u2013Krook Model"},"content":{"rendered":"\n Abstract:<\/strong><\/p>\n\n\n\n This talk presents adaptive sparse-grid discontinuous Galerkin (DG) discretizations for the Bhatnagar\u2013Gross\u2013Krook (BGK) model, a kinetic equation posed in four- and six-dimensional phase-space. Standard DG methods are rendered impractical for the BGK model by the curse of dimensionality, motivating compressed representations that adapt to the solution in time. Using the adaptive sparse-grid DG method, we quantify accuracy and compression by comparing the adaptive degrees of freedom to full-grid DG methods and by assessing the resulting kinetic and fluid quantities in both fluid and rarefied regimes. Test cases include a relaxation problem, a multidimensional Sod shock tube, and shear\/expansion flows used in prior low-rank BGK studies. To build an efficient Maxwellian evaluation without violating conservation, a central obstacle for structure-persevering BGK simulations, we introduce a hybrid interpolation strategy that exploits velocity separability to recover the correct discrete collision invariants and prove conservation of the resulting discrete collision operator on adaptive sparse grids. The results show that the adaptive sparse-grid strategy can recover accurate and physically relevant solutions with sharp gradients, and the method reduces the active degrees of freedom by factors ranging from several-fold to several orders of magnitude, with the largest reductions occurring in the six-dimensional examples. All computations are performed with the open-source ASGarD adaptive sparse-grid DG library.<\/p>\n\n\n\n <\/p>\n\n\n\nDr. Miroslav Stoyanov, ORNL<\/h3>\n\n\n\n
Dr. Shaked Regev, ORNL<\/h3>\n\n\n\n
Dr. Stefan Schnake, ORNL<\/h3>\n\n\n\n