Research

Computation plays a critical role in the design and optimization of engineering systems. CCSE researchers develop new formulations, methods, and algorithms that advance next-generation design tools.

Our work focuses on:

• Addressing the computational cost of design loops
• Searching high-dimensional parameter spaces
• Representing and visualizing complex geometries
• Leveraging complementary strengths of data and modeling
• Incorporating uncertainty into design decision-making

Our research is grounded in numerical analysis, mathematical optimization, and computational mathematics.

Our work focuses on:

• Theoretical analysis of complexity and convergence
• Developing fast, scalable algorithms for canonical computational problems with broad applicability
• Implementing new algorithms for advanced hardware architectures and high-performance computing

As society becomes more complex, so do science and engineering challenges—challenges that outstrip available data and standard modeling capabilities. That’s where machine learning (ML) comes in. CCSE research explores connections between ML approaches and scientific computing, enabling predictions and solutions that advance scientific innovation.

Our work focuses on:

• Developing new methods for inverse problems, data assimilation, and broader problems in computational statistics
• Creating predictive “digital twins” of physical systems
• Applying large-scale optimization, numerical algorithms, and ML tools to predictive modeling and high-dimensional statistics
• Advancing uncertainty quantification (UQ) to improve computational predictions in fields from engineering to climate science

Advances in hardware architectures and high-performance computing (HPC) demand the development of new algorithms. These methods maximize the capabilities of modern computing systems and accelerate scientific discovery. Here, computational tools refer both to the mathematical formulations that define an approach and to their software implementations for specific architectures.

Our work focuses on:

• Developing algorithms for advanced hardware architectures and high-performance computing
• Developing open-source scientific software toolchains that enable reproducible science

Computational modeling is often described as the “third paradigm” of scientific discovery, complementing theory and experimentation. CCSE researchers use computational simulation to gain new scientific insights and seek technological innovations.

Our work focuses on:

• Developing computational methods in fluid dynamics, materials science, transportation systems, biological systems, and more
• Formulating new mathematical models that span continuum, molecular, and quantum scales
• Creating advanced simulation methodologies tailored to these models