450 research outputs found
Near-Optimal Primal-Dual Algorithms for Quantity-Based Network Revenue Management
We study the canonical quantity-based network revenue management (NRM)
problem where the decision-maker must irrevocably accept or reject each
arriving customer request with the goal of maximizing the total revenue given
limited resources. The exact solution to the problem by dynamic programming is
computationally intractable due to the well-known curse of dimensionality.
Existing works in the literature make use of the solution to the deterministic
linear program (DLP) to design asymptotically optimal algorithms. Those
algorithms rely on repeatedly solving DLPs to achieve near-optimal regret
bounds. It is, however, time-consuming to repeatedly compute the DLP solutions
in real time, especially in large-scale problems that may involve hundreds of
millions of demand units. In this paper, we propose innovative algorithms for
the NRM problem that are easy to implement and do not require solving any DLPs.
Our algorithm achieves a regret bound of , where is the system
size. To the best of our knowledge, this is the first NRM algorithm that (i)
has an asymptotic regret bound, and (ii) does not require solving
any DLPs
Generalizing Graph ODE for Learning Complex System Dynamics across Environments
Learning multi-agent system dynamics has been extensively studied for various
real-world applications, such as molecular dynamics in biology. Most of the
existing models are built to learn single system dynamics from observed
historical data and predict the future trajectory. In practice, however, we
might observe multiple systems that are generated across different
environments, which differ in latent exogenous factors such as temperature and
gravity. One simple solution is to learn multiple environment-specific models,
but it fails to exploit the potential commonalities among the dynamics across
environments and offers poor prediction results where per-environment data is
sparse or limited. Here, we present GG-ODE (Generalized Graph Ordinary
Differential Equations), a machine learning framework for learning continuous
multi-agent system dynamics across environments. Our model learns system
dynamics using neural ordinary differential equations (ODE) parameterized by
Graph Neural Networks (GNNs) to capture the continuous interaction among
agents. We achieve the model generalization by assuming the dynamics across
different environments are governed by common physics laws that can be captured
via learning a shared ODE function. The distinct latent exogenous factors
learned for each environment are incorporated into the ODE function to account
for their differences. To improve model performance, we additionally design two
regularization losses to (1) enforce the orthogonality between the learned
initial states and exogenous factors via mutual information minimization; and
(2) reduce the temporal variance of learned exogenous factors within the same
system via contrastive learning. Experiments over various physical simulations
show that our model can accurately predict system dynamics, especially in the
long range, and can generalize well to new systems with few observations
Model development and numerical simulation of thermo-sensitive hydrogel and microgel-based drug delivery
Master'sMASTER OF ENGINEERIN
Graph Neural Networks for Molecules
Graph neural networks (GNNs), which are capable of learning representations
from graphical data, are naturally suitable for modeling molecular systems.
This review introduces GNNs and their various applications for small organic
molecules. GNNs rely on message-passing operations, a generic yet powerful
framework, to update node features iteratively. Many researches design GNN
architectures to effectively learn topological information of 2D molecule
graphs as well as geometric information of 3D molecular systems. GNNs have been
implemented in a wide variety of molecular applications, including molecular
property prediction, molecular scoring and docking, molecular optimization and
de novo generation, molecular dynamics simulation, etc. Besides, the review
also summarizes the recent development of self-supervised learning for
molecules with GNNs.Comment: A chapter for the book "Machine Learning in Molecular Sciences". 31
pages, 4 figure
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