Temporal coarse-graining of latent default paths explains effective correlation in corporate defaults.
problem Understanding effective default correlation in corporate defaults.
method Temporal coarse-graining of latent default-probability paths, applied to corporate default-count data.
result Temporal coarse-graining provides a scale-consistent baseline that improves identifiability and reduces over-allocation of long-horizon fluctuations.
Temporal aggregation reveals latent default correlation from monthly data.
problem Understanding effective default correlation from monthly default data.
method Temporal coarse-graining of latent default-probability paths.
result Temporal coarse-graining improves identifiability and reduces over-allocation of long-horizon fluctuations.
Molecular dynamics simulations provide theoretical insight into the microscopic behavior of materials in condensed phase and, as a predictive tool, enable computational design of new compounds. However, because of the large temporal and spatial scales involved in thermodynamic and kinetic phenomena in materials, atomis…
Temporal coarse-graining of multi-sector default count data generates effective correlation matrices and rank copulas.
problem Explaining the difference in default dependence between monthly and annual aggregation.
method Dynamic low-rank state-space model with AR(1) latent credit-state factors.
result Effective correlation matrices and rank copulas are generated from monthly default count data.
Machine learning generates coarse-grained force fields for molecular dynamics.
problem Creating thermodynamically consistent coarse-grained models for larger systems.
method Hybrid architecture using graph neural networks to learn molecular features.
result Framework reproduces thermodynamics for small biomolecular systems.
GDML learns effective CG models from all-atom data.
problem Learning effective coarse-grained force fields efficiently.
method Ensemble learning with stratified sampling and GDML.
result GDML yields smaller free energy error than neural networks.
Atomistic or ab-initio molecular dynamics simulations are widely used to predict thermodynamics and kinetics and relate them to molecular structure. A common approach to go beyond the time- and length-scales accessible with such computationally expensive simulations is the definition of coarse-grained molecular models.…
Data coarse graining improves model performance by filtering out less relevant features.
problem Lossy data transformations lose information but can improve model generalization.
method Data coarse graining schemes that systematically discard features based on relevance to the learning task.
result A 'high-pass' scheme helps models generalize better by filtering out less relevant features.
This paper models default data to capture dynamic dependence across sectors.
problem Static models fail to explain monthly default dependence.
method Dynamic low-rank state-space model for monthly multi-sector default-count data.
result Effective correlation matrices and copulas are induced from monthly data.
A tensor provides a concise way to codify the interdependence of complex data. Treating a tensor as a d-way array, each entry records the interaction between the different indices. Clustering provides a way to parse the complexity of the data into more readily understandable information. Clustering methods are heavily …
Financial markets analyzed by reducing correlation matrix complexity.
problem Understanding complex financial market correlations.
method Coarse graining Pearson correlation matrices into Guhr matrices by market sectors.
result Significant reduction in the number of relevant variables.
CG-BGs combine flow-based models with PMFs to sample large systems efficiently.
problem Sampling equilibrium molecular configurations from the Boltzmann distribution is challenging.
method Coarse-grained Boltzmann Generators (CG-BGs) use flow-based models and learned PMFs for efficient sampling.
result CG-BGs provide a practical route for sampling larger molecular systems efficiently.
We present a novel learning framework that consistently embeds underlying physics while bypassing a significant drawback of most modern, data-driven coarse-grained approaches in the context of molecular dynamics (MD), i.e., the availability of big data. The generation of a sufficiently large training dataset poses a co…
DiAMoNDBack models protein backmapping from coarse-grained Cα traces.
problem Restoring all-atom details from coarse-grained protein representations.
method Autoregressive denoising diffusion model for residue-by-residue backmapping.
result Achieves state-of-the-art reconstruction performance in diverse applications.
Framework preserves emergent physics in non-equilibrium systems from particle trajectories.
problem Linking short spatiotemporal scales to emergent bulk physics in multiscale systems.
method Metriplectic bracket formalism for structure-preserving coarse-graining.
result Preservation of thermodynamic laws and conservation in machine-learned dynamics.
New method uses normalizing flows to improve force fields for coarse-grained molecular dynamics.
problem Lack of reference atomistic forces makes force matching infeasible for MLCG force fields.
method Introduces noise-based kernels adapted to low-data regimes using normalizing flows.
result Flow-based kernels reduce local distortions while preserving global accuracy.
We propose a probabilistic model for refining coarse-grained spatial data by utilizing auxiliary spatial data sets. Existing methods require that the spatial granularities of the auxiliary data sets are the same as the desired granularity of target data. The proposed model can effectively make use of auxiliary data set…
Sparsity helps reduce the computational complexity of deep neural networks by skipping zeros. Taking advantage of sparsity is listed as a high priority in next generation DNN accelerators such as TPU. The structure of sparsity, i.e., the granularity of pruning, affects the efficiency of hardware accelerator design as w…
Neural HMM with AGA captures multi-scale dynamics in financial markets.
problem Capturing multi-scale temporal dynamics in financial markets.
method Parallel multi-resolution encoders, adaptive gating, and multi-head attention.
result Outperforms fixed-resolution baselines in predicting price movements and liquidity shocks.
Graph neural network predicts optimal coarse-grained mapping operators.
problem Optimal coarse-grained mapping operators selection for molecular dynamics simulations.
method Graph Neural Network (DSGPM) trained on expert-annotated data.
result DSGPM outperforms state-of-the-art methods in graph segmentation.
We propose a new approach for analyzing price fluctuations in their strongly correlated regime ranging from minutes to months. This is done by employing a self-similarity assumption for the magnitude of coarse-grained price fluctuation or volatility. The existence of a Cramer function, the characteristic function for s…
Extracts coarse-grained PDEs from microscopic simulations.
problem Discovering effective PDEs for macro-scale processes from microscopic data.
method Combining neural networks with equation-free numerics and data-driven approaches.
result Efficiently discovers macro-scale PDEs from microscopic simulations.
Survey of weak form's role in equation learning, parameter estimation, and coarse graining.
problem Noise robustness, accuracy, and computational efficiency in weak form applications.
method Survey and recent developments in weak form versions of equation learning, parameter estimation, and coarse graining.
result Surprising noise robustness, accuracy, and computational efficiency in weak form applications.
A new machine-learned CG model predicts protein structures efficiently.
problem Developing a universal, computationally efficient protein simulation model.
method Combining deep learning with all-atom protein simulations to create a transferable CG force field.
result The model predicts protein structures, intermediates, and fluctuations efficiently.
Improved CG force-field learning from all-atom data.
problem Training accurate coarse-grained models from all-atom simulations is challenging.
method Optimized force mapping to improve statistical efficiency of force-field learning.
result Substantially improved CG force-fields can be learned from the same simulation data.
Data-based discovery of effective, coarse-grained (CG) models of high-dimensional dynamical systems presents a unique challenge in computational physics and particularly in the context of multiscale problems. The present paper offers a data-based, probablistic perspective that enables the quantification of predictive u…
The automated construction of coarse-grained models represents a pivotal component in computer simulation of physical systems and is a key enabler in various analysis and design tasks related to uncertainty quantification. Pertinent methods are severely inhibited by the high-dimension of the parametric input and the li…
We propose a data-driven, coarse-graining formulation in the context of equilibrium statistical mechanics. In contrast to existing techniques which are based on a fine-to-coarse map, we adopt the opposite strategy by prescribing a probabilistic coarse-to-fine map. This corresponds to a directed probabilistic model wher…
The recent trend for acquiring big data assumes that possessing quantitatively more and qualitatively finer data necessarily provides an advantage that may be critical in competitive situations. Using a model complex adaptive system where agents compete for a limited resource using information coarse-grained to differe…
Using a recently developed method of noise level estimation that makes use of properties of the coarse grained-entropy we have analyzed the noise level for the Dow Jones index and a few stocks from the New York Stock Exchange. We have found that the noise level ranges from 40 to 80 percent of the signal variance. The c…
We introduce a hierarchical architecture for video understanding that exploits the structure of real world actions by capturing targets at different levels of granularity. We design the model such that it first learns simpler coarse-grained tasks, and then moves on to learn more fine-grained targets. The model is train…
Although there has been a rapid development of practical applications, theoretical explanations of deep learning are in their infancy. Deep learning performs a sophisticated coarse graining. Since coarse graining is a key ingredient of the renormalization group (RG), RG may provide a useful theoretical framework direct…
We present an algorithm for supervised learning using tensor networks, employing a step of preprocessing the data by coarse-graining through a sequence of wavelet transformations. We represent these transformations as a set of tensor network layers identical to those in a multi-scale entanglement renormalization ansatz…
We discuss a Bayesian formulation to coarse-graining (CG) of PDEs where the coefficients (e.g. material parameters) exhibit random, fine scale variability. The direct solution to such problems requires grids that are small enough to resolve this fine scale variability which unavoidably requires the repeated solution of…
MLP residual networks implement a selective coarse-graining procedure governed by the spectral structure of the input distribution.
problem Understanding the coarse-graining procedure in MLP residual networks
method Analyzing a pure MLP residual stack on synthetic Markov chain sequences
result MLP residual networks implement a selective coarse-graining procedure governed by the spectral structure of the input distribution
The paper reduces the complexity of financial market correlation matrices to a 2x2 matrix.
problem Reducing the complexity of financial market correlation matrices for easier analysis.
method Sectorial coarse graining followed by averaging over blocks of stocks.
result Averaging over blocks of stocks results in a reduced matrix with specific properties.
WSINDy identifies reduced Hamiltonian systems from particle interactions.
problem Coarse-graining Hamiltonian dynamics with approximate symmetries.
method WSINDy algorithm applied to Hamiltonian systems with timescale separation.
result WSINDy successfully identifies reduced Hamiltonian systems from noisy data.
The combination of high-dimensionality and disparity of time scales encountered in many problems in computational physics has motivated the development of coarse-grained (CG) models. In this paper, we advocate the paradigm of data-driven discovery for extract- ing governing equations by employing fine-scale simulation …
Develops MgCSL for discovering causal structures in high-dimensional data.
problem Discovering causal relationships from high-dimensional data with complex interplay of variables.
method MgCSL uses sparse auto-encoders for coarse-graining and multi-layer perceptrons for detailed analysis, introducing simplified acyclicity constraints.
result MgCSL outperforms existing methods and finds explainable causal connections in fMRI datasets.
This study uses persistent homology to analyze complex transitional networks from time series data.
problem Lack of effective tools to summarize complex topology in transitional networks.
method Persistent homology from topological data analysis applied to coarse-grained state-space networks (CGSSN).
result CGSSN improves dynamic state detection and noise robustness compared to other methods.
Introduce a thermodynamically informed, temperature-transferable MLCG framework for proteins.
problem Temperature transferability of MLCG models for proteins.
method Explicit decomposition of CG potential into energetic and entropic components.
result Reproduces temperature-dependent quantities like heat capacity.
New CGMD model predicts non-equilibrium processes better than existing methods.
problem Inconsistency in conditional distribution of unresolved variables.
method Time-lagged independent component analysis to minimize entropy contribution of unresolved variables.
result The model's generalization ability for non-equilibrium processes is significantly improved.
The paper develops a physics-aware method for modeling multiscale dynamics with reduced data.
problem Discovering effective, lower-dimensional models for high-dimensional dynamical systems.
method Probabilistic deep neural networks incorporating physical constraints.
result The method reduces the need for extensive multiscale simulations (Small Data regime).
Estimating temporal patterns in travel times along road segments in urban settings is of central importance to traffic engineers and city planners. In this work, we propose a methodology to leverage coarse-grained and aggregated travel time data to estimate the street-level travel times of a given metropolitan area. Ou…
Weakly-supervised learning is a paradigm for alleviating the scarcity of labeled data by leveraging lower-quality but larger-scale supervision signals. While existing work mainly focuses on utilizing a certain type of weak supervision, we present a probabilistic framework, learning from indirect observations, for learn…
Reduced models derived from agent-based systems using Koopman theory.
problem Time-consuming simulations of large agent-based systems.
method Koopman operator theory applied to simulation data.
result Derived reduced models match known analytical results.
A conceptually simple way to classify images is to directly compare test-set data and training-set data. The accuracy of this approach is limited by the method of comparison used, and by the extent to which the training-set data cover configuration space. Here we show that this coverage can be substantially increased u…
We analyze the data of the Italian and U.S. futures on the stock markets and we test the validity of the Continuous Time Random Walk assumption for the survival probability of the returns time series via a renewal aging experiment. We also study the survival probability of returns sign and apply a coarse graining proce…