Algorithm learns latent variables for thermodynamically-consistent deep neural networks.
problem Predicting time evolution of large-scale physical systems with thermodynamic consistency.
method Sparse autoencoders and structure-preserving neural networks.
result Method conserves total energy and entropy inequality for both conservative and dissipative systems.
Develops neural networks that follow thermodynamics principles.
problem Learning physical systems from data while respecting thermodynamics.
method Uses feedforward neural networks and the GENERIC formalism to enforce metriplectic structure.
result Predictions comply with first and second principles of thermodynamics.
Paper proposes G-CRD to improve GNNs by preserving global graph topology.
problem Improving lightweight GNNs for robust performance on large-scale real-world graphs.
method Introduces Graph Contrastive Representation Distillation (G-CRD) using contrastive learning.
result G-CRD consistently boosts GNN performance and robustness, outperforming existing methods.
Deep learning methods are reviewed for preserving structure in neural networks.
problem Challenges in applying deep learning, especially in preserving structure.
method Review of existing deep learning methods and new algorithmic frameworks.
result Mathematical understanding and systematic design of deep learning methods to preserve structure.
Eigen-GNN enhances GNNs by preserving graph structures.
problem Existing shallow GNNs fail to effectively preserve graph structures.
method Integrates eigenspace of graph structures into GNNs as a dimensionality reduction module.
result Eigen-GNN boosts GNNs' ability to preserve graph structures without increasing depth.
This study compares different thermodynamic structure-informed neural networks for solving differential equations.
problem Improving the accuracy and physical consistency of neural network solutions to differential equations.
method Comprehensive evaluation of various thermodynamic formulations in physics-informed neural networks.
result Newtonian-residual-based PINNs fail to reliably recover physical quantities, while structure-preserving formulations enhance accuracy and robustness.
New saddle network architectures preserve convex-concave geometry in optimization problems.
problem Optimization models with convex x and concave y components.
method Structured separable decomposition and saddle network architectures.
result Proven one-dimensional approximation theorem and high accuracy on various test functions.
GraphSAIL updates GNN-based recommender models incrementally to reduce computation time and improve frequent updates.
problem Incremental updates in GNN-based recommender systems are computationally expensive and prone to forgetting.
method GraphSAIL uses a graph structure preservation strategy to update GNN models incrementally, preserving long-term preferences and properties.
result GraphSAIL reduces computation time and improves frequent updates compared to other incremental learning techniques.
Structure-preserving GANs learn distributions with group symmetry efficiently.
problem Learning distributions with group symmetry efficiently.
method Developed structure-preserving GANs by reducing the discriminator space and designing structured generators.
result Significantly improved sample fidelity and diversity in small data regimes.
In this paper we extend some well-known rigidity results for conformal changes of Einstein metrics to the class of generalized quasi-Einstein (GQE) metrics, which includes gradient Ricci solitons. In order to do so, we introduce the notions of conformal diffeomorphisms and vector fields that preserve a GQE structure. W…
Survey explores cohomology's roles in applied math and sciences.
problem Understanding cohomology's role in solving differential equations.
method Examining differential complexes and structure-preserving discretizations.
result Various fundamental concepts in mechanics are formulated using differential complexes.
We present a numerical approach for approximating unknown Hamiltonian systems using observation data. A distinct feature of the proposed method is that it is structure-preserving, in the sense that it enforces conservation of the reconstructed Hamiltonian. This is achieved by directly approximating the underlying unkno…
A fast calibration method for rough volatility models with jumps.
problem Calibrating stochastic volatility models to market data efficiently.
method Structure-preserving approach: split pricing formula, precompute data-independent integrals, and approximate market-dependent remainder with neural networks.
result Calibration achieves high accuracy and speed, and a pure-jump rough volatility model adequately captures VIX dynamics.
We prove an existence result for local and global G-structure preserving affine immersions between affine manifolds. Several examples are discussed in the context of Riemannian and semi-Riemannian geometry, including the case of isometric immersions into Lie groups endowed with a left-invariant metric, and the case of …
Deep networks with orthogonal weights show stable fluctuations, improving generalization and training speed.
problem Fluctuations in deep networks with Gaussian weights can impair training, especially in networks with depth comparable to width.
method Analytical and numerical studies of fully-connected networks with orthogonal weight initialization and tanh activations.
result Rectangular networks with orthogonal weights have stable fluctuations independent of network depth, leading to better generalization and training speed.
Regularization preserves topological data structure in autoencoders.
problem Ensuring topological data structure preservation in autoencoders.
method Regularization using Legendre nodes to preserve manifold embedding.
result Regularized autoencoders ensure one-to-one embedding of data manifolds.
Parametric UMAP learns a mapping from data to embeddings.
problem Representing and learning from structured data.
method Parametric optimization over neural network weights for UMAP.
result Parametric UMAP performs comparably to non-parametric UMAP with faster online embeddings.
A new RNN model tackles long-time dependencies with fast, invertible, and memory-efficient hidden states.
problem Challenges in processing sequential inputs with long-time dependencies in RNNs.
method A novel RNN architecture based on a Hamiltonian system of oscillators.
result The proposed RNN mitigates exploding and vanishing gradient problems, providing state-of-the-art performance.
A new method learns Hamiltonian functions from noisy data.
problem Learning Hamiltonian functions from noisy observations.
method Structure-preserving kernel ridge regression method.
result The method yields excellent numerical performances.
This paper is the first work to propose a network to predict a structured uncertainty distribution for a synthesized image. Previous approaches have been mostly limited to predicting diagonal covariance matrices. Our novel model learns to predict a full Gaussian covariance matrix for each reconstruction, which permits …
A fast method learns plasma collision kernels from simulations, improving kinetic models.
problem Improving kinetic models for plasma dynamics beyond the weakly coupled regime.
method Data-driven collisional operator, fast spectral separation method.
result Accurately captures plasma dynamics in moderately coupled regime.
New method preserves MHD equations on sphere without costly matrix exponentials.
problem Discretizing MHD equations on sphere for numerical simulations.
method Lie-Poisson discretization, geometric quantization, semi-direct product Lie algebras.
result Preserves Lie-Poisson structure and Casimir functions.
Multi-task learning (MTL) improves prediction performance in different contexts by learning models jointly on multiple different, but related tasks. Network data, which are a priori data with a rich relational structure, provide an important context for applying MTL. In particular, the explicit relational structure imp…
A new measure of causal influence quantifies intrinsic contributions in DAGs.
problem Quantifying intrinsic causal contributions in Directed Acyclic Graphs (DAGs).
method Recursive decomposition of node contributions, structure-preserving interventions, Shapley symmetrization.
result A measure of intrinsic causal contribution that is invariant to node relabeling.
Optimal transport for vector Gaussian mixtures improves efficiency and structure preservation.
problem Optimal mass transport for vector-valued Gaussian mixtures.
method Vectorizing Gaussian mixture models and studying optimal mass transport problems.
result Computational efficiency and structure preservation in optimal mass transport.
Graph transformers outperform graph convolutions by preserving community information.
problem Understanding why graph transformers perform well in node-level prediction tasks.
method Analyzing the Gaussian process limits of graph transformers with infinite width and infinite heads.
result Graph transformers maintain discriminative node representations even in deep layers, preventing oversmoothing.
This paper introduces hierarchical quasi-clustering methods, a generalization of hierarchical clustering for asymmetric networks where the output structure preserves the asymmetry of the input data. We show that this output structure is equivalent to a finite quasi-ultrametric space and study admissibility with respect…
New integrators for mechanical systems on Lie groups simplify based on group properties.
problem Designing numerical integrators for mechanical systems on Lie groups.
method Leverage retraction maps and Lie group properties to design structure-preserving integrators.
result Simplified design of integrators for Euler-Poincare and Lie-Poisson equations.
A new method clusters complex networks using topological and geometric structure.
problem Clustering complex networks with intricate topology.
method Centroid-based clustering strategy using Wasserstein distance and barycenter for persistence barcodes.
result Demonstrated effectiveness on simulated and real-world networks.
Develops integrators for nonholonomic systems on Lie groups.
problem Nonholonomic constraints on Lie groups.
method Using retraction maps and Hamel formulation.
result Structure-preserving numerical integrators for nonholonomic systems.
Koopman-PINN framework improves epidemic model parameter inference and forecasting
problem Epidemic model parameter inference and forecasting
method Combining Koopman operator theory and physics-informed learning
result More accurate parameter estimation, trajectory reconstruction, and long-term forecasting
Computed tomography (CT) is widely used in screening, diagnosis, and image-guided therapy for both clinical and research purposes. Since CT involves ionizing radiation, an overarching thrust of related technical research is development of novel methods enabling ultrahigh quality imaging with fine structural details whi…
We develop a method to describe laws of random surfaces using surface holonomy.
problem Describing laws of random surfaces with structure.
method Introduce surface holonomy and develop expected surface developments.
result Expected surface development provides a structured description of random surface laws.
Abstraction of Markov Decision Processes is a useful tool for solving complex problems, as it can ignore unimportant aspects of an environment, simplifying the process of learning an optimal policy. In this paper, we propose a new algorithm for finding abstract MDPs in environments with continuous state spaces. It is b…
We classify nilmanifolds with an invariant symplectic half-flat structure. We solve the half-flat evolution equations in one example, writing down the resulting Ricci-flat metric. We study the geometry of the orbit space of 6-manifolds with an SU(3)-structure preserved by a U(1) action, giving characterizations in the …
New Wasserstein divergence improves generative model robustness and structure preservation.
problem Improving generative model robustness and structure preservation.
method Introduces a novel Wasserstein-1 path-space divergence and a WUP theorem.
result Derives robustness and generalization bounds for flow-based models.
Paper tackles imbalanced time series classification with a novel oversampling method.
problem Imbalanced time series classification challenges due to high dimensionality and correlation.
method Density-ratio based clustering followed by shrinkage technique for covariance estimation, then generating synthetic samples.
result OHIT outperforms state-of-the-art methods in F1, G-mean, and AUC metrics.
A quantum state generation method that respects physical constraints.
problem Generating quantum states with complex-valued Hermitian, positive semi-definite, and trace one properties.
method Mirror diffusion model with von Neumann entropy to enforce structural constraints.
result Demonstrated effective generation of quantum states with conditional guidance.
Derives stochastic and dissipative dynamics preserving Gibbs measure.
problem Understanding and deriving structure-preserving stochastic systems.
method Extension of Hamilton-Pontryagin principle, symmetry reduction, and inclusion of dissipation.
result New derivation of double-bracket dissipation.
Develops integrators for Hamiltonian systems in Jacobi manifolds.
problem Modeling conservative systems with dissipative and thermodynamic phenomena.
method Constructs structure-preserving integrators for Hamiltonian systems in Jacobi manifolds.
result Proposes a numerical integration technique compatible with Jacobi dynamics.
CDSPP learns domain-specific projections for heterogeneous domain adaptation.
problem Heterogeneous domain adaptation problems where source and target domains have different modalities or feature dimensions.
method Cross-Domain Structure Preserving Projection (CDSPP) algorithm that learns domain-specific projections to map features into a common subspace.
result CDSPP achieves superior performance in both supervised and semi-supervised HDA compared to state-of-the-art methods.
We establish a connection between recent developments in the study of vortices in the abelian Higgs models, and in the theory of structure-preserving discrete conformal maps. We explain how both are related via conformal mapping problems involving prescribed linear combinations of the curvature and volume form, and sho…
Develops a new tensor classification method for high-dimensional data.
problem Efficient learning algorithms exploiting tensorial structure in high-dimensional multi-way arrays.
method Tensor Train Multi-way Multi-level Kernel (TT-MMK) combining Canonical Polyadic decomposition, Dual Structure-preserving Support Vector Machine, and Tensor Train approximation.
result The TT-MMK method provides higher prediction accuracy and is more reliable computationally compared to other techniques.
GCML preserves geometric structure in manifold clustering for diverse data types.
problem Loss functions in manifold clustering can corrupt latent space structure.
method GCML framework with isometric and ranking losses for geometric structure preservation.
result GCML outperforms other methods in latent space structure preservation and performance metrics.
This method infers models from data with physical insights, minimizing model order.
problem Learning models from data while preserving physical insights.
method Structure preservation and rank minimization via Sylvester equations.
result Models of low order are obtained with fewer degrees of freedom.
We discuss the nature of structure-preserving maps of varies function algebras. In particular, we identify isomorphisms between special Colombeau algebras on manifolds with invertible manifold-valued generalized functions in the case of smooth parametrization. As a consequence, and to underline the consistency and vali…
Suffering from the multi-view data diversity and complexity for semi-supervised classification, most of existing graph convolutional networks focus on the networks architecture construction or the salient graph structure preservation, and ignore the the complete graph structure for semi-supervised classification contri…
A new ML method predicts long-time-step molecular dynamics, preserving symplectic and time-reversible properties.
problem Limited computational efficiency in long-time-step molecular dynamics simulations.
method Learning data-driven structure-preserving maps to generate long time-step classical dynamics.
result The method eliminates artifacts like lack of energy conservation and loss of equipartition.