Date: April 18, 2026
Location: MATH 175
Invited Speaker: Prof. Rongjie Lai
We are pleased to host the Third Annual Purdue SIAM Student Conference on April 18, 2026 in MATH 175. The conference features 20-minute talks by graduate students and postdocs working in computational, industrial, and applied mathematics. Coffee, lunch, and a light breakfast will be provided.
This year's invited speaker is Prof. Rongjie Lai (bio below).
We encourage students in the Math, CS, Statistics, ECE, ME, and IE departments to attend.
Time: 10:10 – 11:00 AM
Title: Can Deep Networks Overcome the Curse of Dimensionality? A Complexity Perspective
Abstract: Deep artificial neural networks (DNNs) have achieved remarkable success across various scientific and engineering domains. A fundamental question that arises is whether DNNs can overcome the curse of dimensionality. This talk discusses approximation and generalization analyses that reveal how the complexity of DNNs depends on dimensionality. Through three key examples, the complexity of DNNs is shown to scale exponentially with the intrinsic dimension rather than the ambient space dimension: (1) DNNs learning low-dimensional manifold structures from high-dimensional data; (2) neural operator learning for optimal control and mean-field control; and (3) neural operator learning for dynamical systems. These results provide insights into the power and limitations of deep networks in high-dimensional settings.
About the Speaker: Prof. Rongjie Lai is a leading figure in applied and computational mathematics at Purdue University. His research develops mathematical and computational frameworks for imaging, data science, geometric learning, and analysis of manifold-structured data, with broad impact across variational PDEs, optimization, and machine learning. He has published over 80 peer-reviewed works with significant citations in operator learning, mean-field games, and geometric methods. His contributions have been supported by major grants, including an NSF CAREER Award, NSF's SCALE MoDL program, and NIH-sponsored projects, along with industry collaborations.
See invited speaker section above for details.
We study finite-sum nonlinear programs with localized variable coupling encoded by a (hyper)graph. A graph-compliant decomposition framework brings message passing into continuous optimization in a rigorous, implementable, and provable way. The (hyper)graph is partitioned into tree clusters (hypertree factor graphs); at each iteration, agents update in parallel by solving local subproblems whose objective splits into an intra-cluster term summarized by cost-to-go messages from one min-sum sweep and an inter-cluster coupling term handled Jacobi-style. The method supports graph-compliant surrogates and surrogate hyperedge splitting. We establish convergence for (strongly) convex and nonconvex objectives with topology- and partition-explicit rates. To our knowledge, this is the first convergent message-passing method on loopy graphs.
Keywords: Distributed optimization, Graph decomposition, Message passing, Block Jacobi, Hypergraph
We study decentralized optimization over networks, where agents minimize a sum of locally smooth (strongly) convex losses plus a nonsmooth convex extended-value term. Agents adaptively adjust their stepsize via local backtracking coupled with lightweight min-consensus protocols. The design stems from a three-operator splitting factorization with a new BCV preconditioning metric. Under mere convexity the methods converge sublinearly; under strong convexity of the sum and partial smoothness of the nonsmooth component, linear convergence is proved. Numerical experiments corroborate the theory.
How many genetic variations actually drive a disease like schizophrenia or a trait like height? Modern genetic studies provide massive amounts of data, but true biological signals are often blurred by "Linkage Disequilibrium" — a natural correlation where neighboring genes are inherited together. This talk explores how mathematical modeling deblurs this data to isolate true genetic drivers from background noise, ensuring the tools scientists use to decode human health are accurate and reliable.
This paper addresses sparse regression vector estimation in the presence of corrupted samples, focusing on accurate support identification. Traditional methods such as LASSO often fail and exhibit inconsistency. We propose a combinatorial, non-convex, and robust LASSO variant supported by theoretical guarantees establishing reliability and robustness, including under heavy-tailed corruption with only a few bounded moments. Extensive experiments validate the theory and compare against LASSO and its robust variants.
Approximating PDE solutions by continuous piecewise linear functions is the core of Finite Element Methods. Shallow ReLU networks generate continuous piecewise linear functions whose mesh points are parameters — so optimizing a network moves the mesh. This is useful when solutions are discontinuous and the interface is unknown, but moving the mesh is computationally intensive. The talk discusses these difficulties and how to overcome them.
Symmetry is a common feature in engineered objects and crucially affects their vibration and waveguiding properties. This talk explores the connection between symmetry and dynamics through wave propagation in prismatic rods. Group- and representation-theoretic concepts classify wave modes by the symmetries in their displacement fields; familiar symmetric and antisymmetric modes emerge as special cases. A symmetry-adapted finite element method reduces computation time by up to 30% in cases where standard periodic boundary conditions are suboptimal.
Angiogenesis plays a crucial role in development, wound healing, and diseases such as cancer. This work studies angiogenesis in an in vivo setting, computing VEGF transport inside a growing chick embryo and analyzing how tissue growth shapes its spatial distribution. The evolving vascular geometry is obtained from time-lapse images and represented implicitly via a phase-field formulation, tracking complex topological changes without mesh regeneration. Simulations show that tissue growth significantly influences VEGF distribution.