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I am interested in the broad area of computational science and engineering with a strong focus on mechanics, model order reduction and scientific machine learning. As such, my research is interdisciplinary, both with respect to computational-science domains and real-life engineering applications. Ongoing and past research has been on the development of high-performance computational models and methods for coupled problems of multiscale nature. A complete list of publications can be found on my Google Scholar profile.
Research Topic #1: Nonlinear dimensionality and model reduction
The computational bottleneck in aerospace engineering often stems from the immense complexity of high-fidelity simulations, where modeling a single jet engine or a hypersonic vehicle can involve millions of degrees of freedom. Traditionally, we have relied on linear reduced-order models to compress this data, but these flat approximations fail to capture the critical, moving physics of flight.
To overcome this rigid construction, our research leverages nonlinear dimensionality reduction to find the intrinsic, curved "manifolds" where the true physics lives. By employing quadratic manifolds, we allow the mathematical representation of the flow field to bend and stretch, capturing sharp gradients and high-frequency features with far fewer variables than traditional methods. This geometric flexibility ensures that the reduced model remains anchored to the underlying physical manifold, even as the system transitions through vastly different flight regimes. It transforms the way we approximate complex systems by recognizing that nature’s most interesting phenomena rarely follow a straight line.
Building on this nonlinear foundation, we utilize dynamic subspace approximations in which the basis vectors are no longer static. Instead of forcing the simulation to occur within a frozen coordinate system, we allow the "mathematical scaffold" to evolve in time alongside the physical solution. This time-dependent approach allows the reduced-order model to "track" the action as it moves through the domain, much like a camera lens that pivots to keep a high-speed projectile in perfect focus. By integrating these evolving bases with rigorous data-driven learning, we enable the creation of ROMs capable of providing the real-time predictive power of a supercomputer directly on flight hardware.
Figure: Dynamic subspace approximation of a traveling wave in 1-D. The model contains only 20 degrees of freedom.
Figure: Turbulent airfoil wake Large Eddy Simulation (LES). Reduced-dimensional modeling of a NACA-0012 airfoil at a Reynolds number of Re=23,000. POD subspace approximation (top) compared a quadratic manifold approximation computed using Riemannian optimization (bottom) at 20 degrees of freedom.
Research Topic #2: Modeling pervasive fracture across the scales
The study of fracture remains a cornerstone of computational solid mechanics, yet it presents a formidable challenge: capturing the delicate interplay between macroscopic structural response and the microscopic failure processes concentrated at a crack tip. During my doctoral research at Duke University, I focused on bridging these disparate spatial scales to enable the high-fidelity modeling of pervasive material failure. While the search for a universal framework is ongoing, variational fracture models have emerged as a powerful solution due to their unified treatment of crack onset and space-time evolution. My work seeks to move beyond the limitations of the traditional Griffith regime, where stresses and strains often become unphysically infinite as the model is refined. By postulating a variational description tailored specifically for cohesive fracture mechanics, we can maintain physical consistency even as we regularize the crack geometry.
A primary hurdle in these "smeared crack" approaches is the precise identification of the sharp crack surface within a diffuse damage field. I revisited this problem through the lens of optimization, utilizing an auxiliary damage field to sharpen our view of the failure interface without sacrificing the mathematical elegance of the variational framework. Because these fracture problems are notoriously computationally expensive, I also developed a scalable and performant implementation of a scale-bridging extended finite element method. This approach provides the necessary relief for the sheer numerical cost of resolving complex geometric features across scales, effectively bringing the predictive power of advanced fracture mechanics to large-scale engineering applications.
Figure: Phase-field simulation of blast impact on a thick steel cylinder.
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