Validated continuation over large parameter ranges for equilibria of PDEs. - Marcio Gameiro; Jean-Philippe Lessard; Konstantin Mischaikow (Math. Comput. Simul., 2008)

Rigorous computation of smooth branches of equilibria for the three dimensional Cahn-Hilliard equation. - Marcio Gameiro; Jean-Philippe Lessard (Numerische Mathematik, 2011)

Efficient Rigorous Numerics for Higher-Dimensional PDEs via One-Dimensional Estimates. - Marcio Gameiro; Jean-Philippe Lessard (SIAM J. Numer. Anal., 2013)

Continuation of Point Clouds via Persistence Diagrams. - Marcio Gameiro; Yasuaki Hiraoka; Ippei Obayashi (CoRR, 2015)

Computation of Smooth Manifolds Via Rigorous Multi-parameter Continuation in Infinite Dimensions. - Marcio Gameiro; Jean-Philippe Lessard; Alessandro Pugliese (Found. Comput. Math., 2016)

Rigorous numerics for piecewise-smooth systems: A functional analytic approach based on Chebyshev series. - Marcio Gameiro; Jean-Philippe Lessard; Yann Ricaud (J. Comput. Appl. Math., 2016)

A Framework for the Numerical Computation and A Posteriori Verification of Invariant Objects of Evolution Equations. - Jordi-Lluís Figueras; Marcio Gameiro; Jean-Philippe Lessard; Rafael de la Llave (SIAM J. Appl. Dyn. Syst., 2017)

A Posteriori Verification of Invariant Objects of Evolution Equations: Periodic Orbits in the Kuramoto-Sivashinsky PDE. - Marcio Gameiro; Jean-Philippe Lessard (SIAM J. Appl. Dyn. Syst., 2017)

Hyperparameter Optimization of Topological Features for Machine Learning Applications. - Francis C. Motta; John Harer; Nick Leiby; Franco Marinozzi; Scott Novotney; Gabe Rocklin; Jed Singer; Devin Strickland; Matt Vaughn; Christopher J. Tralie; Rossella Bedini; Fabiano Bini; et al. (ICMLA, 2019)

Extracting Global Dynamics of Loss Landscape in Deep Learning Models. - Mohammed Eslami; Hamed Eramian; Marcio Gameiro; William D. Kalies; Konstantin Mischaikow (CoRR, 2021)

Parameter estimation in systems exhibiting spatially complex solutions via persistent homology and machine learning. - Sabrina S. Calcina; Marcio Gameiro (Math. Comput. Simul., 2021)

Mapping parameter spaces of biological switches. - Rocky Diegmiller; Lun Zhang; Marcio Gameiro; Justinn Barr; Jasmin Imran Alsous; Paul Schedl; Stanislav Y. Shvartsman; Konstantin Mischaikow (PLoS Comput. Biol., 2021)

Rational design of complex phenotype via network models. - Marcio Gameiro; Tomás Gedeon; Shane Kepley; Konstantin Mischaikow (PLoS Comput. Biol., 2021)

Morse Graphs: Topological Tools for Analyzing the Global Dynamics of Robot Controllers. - Ewerton R. Vieira; Edgar Granados; Aravind Sivaramakrishnan; Marcio Gameiro; Konstantin Mischaikow; Kostas E. Bekris (WAFR, 2022)

A combinatorial marching hypercubes algorithm. - Antonio Castelo; Lucas Moutinho Bueno; Marcio Gameiro (Comput. Graph., 2022)

Extending Combinatorial Regulatory Network Modeling to Include Activity Control and Decay Modulation. - Bree Cummins; Marcio Gameiro; Tomás Gedeon; Shane Kepley; Konstantin Mischaikow; Lun Zhang (SIAM J. Appl. Dyn. Syst., 2022)

Experimental guidance for discovering genetic networks through hypothesis reduction on time series. - Breschine Cummins; Francis C. Motta; Robert C. Moseley; Anastasia Deckard; Sophia Campione; Marcio Gameiro; Tomás Gedeon; Konstantin Mischaikow; Steven B. Haase (PLoS Comput. Biol., 2022)

Data-Efficient Characterization of the Global Dynamics of Robot Controllers with Confidence Guarantees. - Ewerton R. Vieira; Aravind Sivaramakrishnan; Yao Song; Edgar Granados; Marcio Gameiro; Konstantin Mischaikow; Ying Hung; Kostas E. Bekris (ICRA, 2023)

A framework for rigorous computational methods using Haar wavelets for differential equations. - Guilherme Nakassima; Marcio Gameiro (CoRR, 2023)

Identifying Nonlinear Dynamics with High Confidence from Sparse Data. - Bogdan Batko; Marcio Gameiro; Ying Hung; William D. Kalies; Konstantin Mischaikow; Ewerton R. Vieira (SIAM J. Appl. Dyn. Syst., 2024)

A generalized combinatorial marching hypercube algorithm. - Antonio Castelo; Guilherme Nakassima; Lucas Moutinho Bueno; Marcio Gameiro (Comput. Appl. Math., 2024)

Toward Computational Morse-Floer Homology: Forcing Results for Connecting Orbits by Computing Relative Indices of Critical Points. - Jan Bouwe van den Berg; Marcio Gameiro; Jean-Philippe Lessard; Rob Van der Vorst (Found. Comput. Math., 2024)

A fast high-dimensional continuation hypercubes algorithm. - Lucas Martinelli Reia; Marcio Gameiro; Tomás Bueno Moraes Ribeiro; Antonio Castelo (Comput. Graph., 2025)