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This paper introduces a differential dynamic programming (DDP) based framework for polynomial trajectory generation for differentially flat systems. In particular, instead of using a linear equation with increasing size to represent…
Symbolic regression (SR) is the process of discovering hidden relationships from data with mathematical expressions, which is considered an effective way to reach interpretable machine learning (ML). Genetic programming (GP) has been the…
We introduce a new algorithm to solve constrained nonlinear optimal control problem, with an emphasis on low-thrust trajectory in highly nonlinear dynamics. The algorithm, dubbed Pontryagin-Bellman Differential Dynamic Programming (PDDP),…
Despite the recent advances in various Structural Genomics Projects, a large gap remains between the number of sequenced and structurally characterized proteins. Some reasons for this discrepancy include technical difficulties, labor, and…
Protein structural alignment is an important problem in computational biology. In this paper, we present first successes on provably optimal pairwise alignment of protein inter-residue distance matrices, using the popular Dali scoring…
Molecular structure has important applications in many fields. For example, some studies show that molecular spatial information can be used to achieve better prediction results when predicting molecular properties. However, traditional…
Crystal structure prediction (CSP) for inorganic materials is one of the central and most challenging problems in materials science and computational chemistry. This problem can be formulated as a global optimization problem in which global…
We extend a primal-dual fixed point algorithm (PDFP) proposed in [5] to solve two kinds of separable multi-block minimization problems, arising in signal processing and imaging science. This work shows the flexibility of applying PDFP…
Deep learning methods have access to be employed for solving physical systems governed by parametric partial differential equations (PDEs) due to massive scientific data. It has been refined to operator learning that focuses on learning…
The Ordered Covering Problem (OCP) arises in the context of the Discretizable Molecular Distance Geometry Problem (DMDGP), where the ordering of pruning edges significantly impacts the performance of the SBBU algorithm for protein structure…
Gaussian Process (GP) regression is a powerful nonparametric Bayesian framework, but its performance depends critically on the choice of covariance kernel. Selecting an appropriate kernel is therefore central to model quality, yet remains…
Accurate and uncertainty-aware degradation estimation is essential for predictive maintenance in safety-critical systems like rotating machinery with rolling-element bearings. Many existing uncertainty methods lack confidence calibration,…
Bayesian neural networks (BNN) and deep ensembles are principled approaches to estimate the predictive uncertainty of a deep learning model. However their practicality in real-time, industrial-scale applications are limited due to their…
Parameter retrieval and model inversion are key problems in remote sensing and Earth observation. Currently, different approximations exist: a direct, yet costly, inversion of radiative transfer models (RTMs); the statistical inversion with…
We consider solving high-order semidefinite programming (SDP) relaxations of nonconvex polynomial optimization problems (POPs) that often admit degenerate rank-one optimal solutions. Instead of solving the SDP alone, we propose a new…
Solving linear programs is often a challenging task in distributed settings. While there are good algorithms for solving packing and covering linear programs in a distributed manner (Kuhn et al.~2006), this is essentially the only class of…
The rapidly growing parameter volume of deep neural networks (DNNs) hinders the artificial intelligence applications on resource constrained devices, such as mobile and wearable devices. Neural network pruning, as one of the mainstream…
The problem of determining the configuration of points from partial distance information, known as the Euclidean Distance Geometry (EDG) problem, is fundamental to many tasks in the applied sciences. In this paper, we propose two algorithms…
Graphs are versatile tools for representing structured data. As a result, a variety of machine learning methods have been studied for graph data analysis. Although many such learning methods depend on the measurement of differences between…
Machine learning algorithms have been effectively applied into various real world tasks. However, it is difficult to provide high-quality machine learning solutions to accommodate an unknown distribution of input datasets; this difficulty…