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In this work, we further develop multigoal-oriented a posteriori error estimation with two objectives in mind. First, we formulate goal-oriented mesh adaptivity for multiple functionals of interest for nonlinear problems in which both the…
Few-Shot Learning (FSL) is a challenging task, \emph{i.e.}, how to recognize novel classes with few examples? Pre-training based methods effectively tackle the problem by pre-training a feature extractor and then predicting novel classes…
Scientific machine learning is an emerging field that broadly describes the combination of scientific computing and machine learning to address challenges in science and engineering. Within the context of differential equations, this has…
We present a novel approach (DyNODE) that captures the underlying dynamics of a system by incorporating control in a neural ordinary differential equation framework. We conduct a systematic evaluation and comparison of our method and…
We study few-shot learning in natural language domains. Compared to many existing works that apply either metric-based or optimization-based meta-learning to image domain with low inter-task variance, we consider a more realistic setting,…
We formulate an Alternating Direction Method of Mul-tipliers (ADMM) that systematically distributes the computations of any technique for optimizing pairwise functions, including non-submodular potentials. Such discrete functions are very…
Meta-learning has been widely used for implementing few-shot learning and fast model adaptation. One kind of meta-learning methods attempt to learn how to control the gradient descent process in order to make the gradient-based learning…
Modeling of microlensing events poses computational challenges for the resolution of the lens equation and the high dimensionality of the parameter space. In particular, numerical noise represents a severe limitation to fast and efficient…
Neural ordinary differential equations (NODEs) -- parametrizations of differential equations using neural networks -- have shown tremendous promise in learning models of unknown continuous-time dynamical systems from data. However, every…
The neural ordinary differential equation (neural ODE) model has attracted increasing attention in time series analysis for its capability to process irregular time steps, i.e., data are not observed over equally-spaced time intervals. In…
Conventional training of deep neural networks usually requires a substantial amount of data with expensive human annotations. In this paper, we utilize the idea of meta-learning to explain two very different streams of few-shot learning,…
Attention-based learning for fine-grained image recognition remains a challenging task, where most of the existing methods treat each object part in isolation, while neglecting the correlations among them. In addition, the multi-stage or…
Distributed optimization consists of multiple computation nodes working together to minimize a common objective function through local computation iterations and network-constrained communication steps. In the context of robotics,…
Neural differential equations offer a powerful approach for learning dynamics from data. However, they do not impose known constraints that should be obeyed by the learned model. It is well-known that enforcing constraints in surrogate…
In this paper, we present a novel framework to solve differential equations based on multilayer feedforward network. Previous works indicate that solvers based on neural network have low accuracy due to that the boundary conditions are not…
Inverse problem or parameter estimation of ordinary differential equations (ODEs), the iterative process of minimizing the mismatch between model-predicted and experimental states by tuning the parameter values within an optimization…
Methods that align distributions by minimizing an adversarial distance between them have recently achieved impressive results. However, these approaches are difficult to optimize with gradient descent and they often do not converge well…
Chemical reactions modeled by ordinary differential equations are finite-dimensional dissipative dynamical systems with multiple time-scales. They are numerically hard to tackle -- especially when they enter an optimal control problem as…
Boundary value problems in ODEs arise in modelling many physical situations from microscale to mega scale. Such two-point boundary value problems (BVPs) are complex and often possess no analytical closed form solutions. So, one has to rely…
Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…