Machine learning aids excited-state molecular dynamics studies.
problem Challenges in studying electronically excited states of molecules.
method Employing machine learning techniques for excited-state molecular dynamics.
result Highlight successes and challenges in machine learning for excited-state processes.
The excited states of polyatomic systems are rather complex, and often exhibit meta-stable dynamical behaviors. Static analysis of reaction pathway often fails to sufficiently characterize excited state motions due to their highly non-equilibrium nature. Here, we proposed a time series guided clustering algorithm to ge…
Machine learning speeds up quantum chemical calculations of excited states.
problem Accurate quantum chemical calculations of excited states are computationally expensive.
method Employing machine learning to speed up and advance excited-state simulations in various fields.
result Machine learning techniques can significantly reduce computational time for excited-state simulations.
Develops machine learning models for excited states of CH2NH2+.
problem Accurately predicting excited-state properties and couplings for CH2NH2+.
method Combines neural networks and kernel ridge regression, encoding electronic states in inputs.
result Improved accuracy in predicting excited-state properties and couplings.
Paper explores ML for UV spectra, showing transferability in chemical space.
problem Modeling excited states and predicting properties of unseen molecules.
method Adapting charge model for excited states, using SchNarc approach.
result ML models can predict properties of unseen molecules and different excited states.
Deep QMC method accurately computes electronic excited states.
problem Accurate calculation of electronic excited states in large systems.
method Extends variational QMC with deep neural networks for excited states.
result Consistently achieves high accuracy for low-lying excited states.
SchNarc combines SchNet and SHARC for efficient photodynamics simulations.
problem Efficiently simulate excited-state dynamics of complex molecules.
method Combines SchNet for multiple electronic states with SHARC for molecular dynamics, learning energies, forces, and couplings.
result Paves the way for efficient photodynamics simulations of complex systems.
We prove sharp pointwise decay estimates for critical Dirac equations on Rn with n≥2. They appear for instance in the study of critical Dirac equations on compact spin manifolds, describing blow-up profiles, and as effective equations in honeycomb structures. For the latter case, we find excited state…
Photo-induced processes are fundamental in nature, but accurate simulations are seriously limited by the cost of the underlying quantum chemical calculations, hampering their application for long time scales. Here we introduce a method based on machine learning to overcome this bottleneck and enable accurate photodynam…
In this paper, we examine Kitaev's lattice model for an arbitrary complex, semisimple Hopf algebra. We prove that this model gives the same topological invariants as Turaev-Viro theory. Using the description of Turaev-Viro theory as an extended TQFT, we prove that the excited states of the Kitaev model correspond to Tu…
The generalized 5D Black-Scholes differential equation with stochastic volatility is derived. The projections of the stochastic evolutions associated with the random variables from an enlarged space or superspace onto an ordinary space can be achieved via higher-dimensional operators. The stochastic nature of the secur…
The Dirac operator d+delta on the Hodge complex of a Riemannian manifold is regarded as an annihilation operator A. On a weighted space L_mu^2 Omega, [A,A*] acts as multiplication by a positive constant on excited states if and only if the logarithm of the measure density of mu satisfies a pair of equations. The equati…
Market strategies minimize Fisher information to minimize risk.
problem Applying minimum Fisher information principle to market dynamics.
method Analytical extension to quantum harmonic oscillator eigenstates and Gibbs distribution.
result Minimizing Fisher information reduces information and risk.
Deep QMC methods use neural networks to solve quantum chemistry problems.
problem Solving the electronic Schrödinger equation from first principles.
method Quantum Monte Carlo with neural network wavefunctions.
result Highly accurate solutions at reduced computational cost.
In Levin-Wen (LW) models, a wide class of exactly solvable discrete models, for two dimensional topological phases, it is relatively easy to describe only single fluxon excitations, but not the charge and dyonic as well as many-fluxon excitations. To incorporate charged and dyonic excitations in (doubled) topological p…
Paper shows leafwise cohomological expression for dynamical zeta functions.
problem Analyzing dynamical zeta functions on foliated dynamical systems.
method Leafwise cohomological approach.
result Leafwise cohomological expression of dynamical zeta functions.
Study on 2-valued dynamics on complex plane, showing some dynamics can't be group actions.
problem Whether 2-valued dynamics can be defined by the action of a 2-valued group.
method Construction of examples of dynamics that are or are not group actions.
result Some 2-valued dynamics on complex plane cannot be defined by the action of a 2-valued group.
The paper studies dynamic star-shaped risk measures and their representation.
problem Representing dynamic star-shaped risk measures and their properties.
method Representation theorems for dynamic monetary and star-shaped risk measures.
result Dynamic star-shaped risk measures can be represented as the lower envelope of a family of dynamic convex risk measures.
Study circles to understand dynamics and rigidity in homogeneous spaces.
problem Understanding dynamics and rigidity in infinite-volume homogeneous spaces.
method Addressing four questions about circle packings.
result Highlighting the interplay between dynamics, geometry, and rigidity.
Paper connects dynamics of mechanical systems to Reeb dynamics.
problem Understanding dynamics in mechanical systems with Poisson structures.
method Using Jacobi bundle metrics and linear Poisson structures.
result Extends classical results on Reeb dynamics to mechanical systems.
Two heuristics solve dynamic multiple travelling salesmen problems.
problem Dynamic routing with unknown customers.
method Balanced dynamic closest vehicle heuristic and balanced dynamic assignment vehicle heuristic.
result Continuous approximation models for strategic dynamic routing.
In this paper we present a theoretical framework for studying coherent acceptability indices in a dynamic setup. We study dynamic coherent acceptability indices and dynamic coherent risk measures, and we establish a duality between them. We derive a representation theorem for dynamic coherent risk measures in terms of …
DOODL learns shared spectral dynamics across related dynamical systems.
problem Learning independent dynamical operators for each system limits discovery of shared structure.
method DOODL learns a dictionary of characteristic spectral dynamics on a manifold of related systems.
result DOODL achieves errors one to two orders of magnitude lower than independent operator estimation methods.
We propose a new class of mappings, called Dynamic Limit Growth Indices, that are designed to measure the long-run performance of a financial portfolio in discrete time setup. We study various important properties for this new class of measures, and in particular, we provide necessary and sufficient condition for a Dyn…
SPICE estimates sparse linear dynamic networks without hyperparameters.
problem Estimating topology and dynamics of sparse linear dynamic networks.
method SPICE (Sparse Iterative Covariance Estimation) method in an iterative framework.
result Directly reveals the underlying topology of the network.
In this paper we present a theoretical framework for determining dynamic ask and bid prices of derivatives using the theory of dynamic coherent acceptability indices in discrete time. We prove a version of the First Fundamental Theorem of Asset Pricing using the dynamic coherent risk measures. We introduce the dynamic …
Dynamical-VAE learns causal dynamics from POMDPs using future information.
problem Learning accurate state representations from partial observations in POMDPs.
method Dynamical Variational Auto-Encoder (DVAE) with hindsight framework.
result DVAE uncovers causal graph more effectively than history-based methods.
Most real world phenomena such as sunlight distribution under a forest canopy, minerals concentration, stock valuation, exhibit nonstationary dynamics i.e. phenomenon variation changes depending on the locality. Nonstationary dynamics pose both theoretical and practical challenges to statistical machine learning algori…
Unified analysis of DLNs using DMFT reveals dynamics of loss convergence and generalization trade-offs.
problem Understanding the overall dynamics of diagonal linear networks (DLNs) in neural network training.
method Dynamical Mean-Field Theory (DMFT) applied to DLNs.
result Derives low-dimensional effective process capturing high-dimensional gradient flow dynamics.
Method learns to map dynamics of different systems.
problem Mapping dynamics of different systems.
method Learned latent dynamical system for mapping.
result Learned correspondences enable imagined motions and bisimulation.
dLDS models neural dynamics as sparse combinations of simpler components.
problem Understanding complex neural dynamics at a population level.
method Proposes a decomposed dynamical system model trained through dictionary learning.
result Model efficiently captures and demix diverse neural dynamics.
Reinforcement learning would enjoy better success on real-world problems if domain knowledge could be imparted to the algorithm by the modelers. Most problems have both hidden state and unknown dynamics. Partially observable Markov decision processes (POMDPs) allow for the modeling of both. Unfortunately, they do not p…
We consider trivializations of second iterated bundles of a Lie group that preserve lifted group structures. With such a trivialization, we elaborate Hamiltonian dynamics on cotangent, Lagrangian dynamics on tangent bundles and, both Hamiltonian and Lagrangian dynamics on Tulczyjew's symplectic space which is tangent o…
Framework for quantifying uncertainty in dynamic processes.
problem Quantifying uncertainty in dynamic stochastic processes.
method Define dynamic uncertainty sets and dynamic robust risk measures.
result Dynamic robust risk measures are time-consistent under specific uncertainty sets.
This survey clarifies dynamic network terminology and reviews GNN models for dynamic networks.
problem Ambiguity in dynamic network terminology and lack of GNN models for dynamic networks.
method Established consistent terminology and notation for dynamic networks, reviewed GNN models.
result Comprehensive survey of dynamic graph neural network models.
Framework infers Langevin dynamics from stochastic observations of latent systems.
problem Inferring non-stationary Langevin dynamics from indirect stochastic observations.
method Non-parametric framework explicitly modeling stochastic observation process and non-stationary latent dynamics.
result Correct inference of non-stationary dynamics requires accounting for non-equilibrium states and observation duration.
The paper introduces a dynamic MVP model using high-frequency financial data.
problem Capturing the dynamics of minimum variance portfolio weights in financial markets.
method Imposes autoregressive structure on MVP processes and uses CLIME and LASSO for estimation.
result Proposes DR-MVP model with established asymptotic properties.
The paper extends Vlasov kinetic theory to time-dependent dynamics using cosymplectic and cocontact manifolds.
problem Extending Vlasov kinetic theory to time-dependent dynamics.
method Introducing geometric kinetic theories within cosymplectic and cocontact manifolds.
result Alternative realizations of cosymplectic and cocontact kinetic theories linked via Poisson/momentum maps.
NDS learns dynamical models with prior knowledge, improving accuracy and efficiency.
problem Learning accurate dynamical models with limited data and varying dynamics.
method Neural Dynamical Systems (NDS) integrates prior knowledge in ODEs with neural networks to estimate parameters and predict states.
result NDS achieves higher accuracy and uses fewer samples compared to other methods.
New method learns population dynamics from snapshots, outperforming existing models.
problem Capturing periodic and other dynamical properties of population dynamics.
method Wasserstein Lagrangian Mechanics (WLM) for learning second-order dynamics from observed marginals.
result WLM outperforms existing methods across various dynamics, including vortex dynamics, embryonic development, and flocking.
Paper uses Chebyshev Tensors for accurate dynamic sensitivities and ISDA SIMM computation.
problem Computing dynamic sensitivities and initial margin for financial instruments.
method Uses Chebyshev Tensors in Monte Carlo simulations to compute dynamic sensitivities and ISDA SIMM.
result High accuracy and computational gains for FX swaps and Spread Options.
Model dynamic customer sensitivities across categories.
problem Dynamic heterogeneity in customer sensitivities to marketing elements.
method Hierarchical dynamic factor model with Bayesian nonparametric Gaussian processes.
result Dynamic heterogeneity can be explained by a few global trends.
Survey on computational models in dynamical systems, including new universality concepts.
problem Understanding the relationship between computational models and dynamical systems.
method Review of recent works on Turing universality, Topological Kleene Field Theories, and dynamical bordisms.
result Introduction of new perspectives on computability through dynamical systems.
FNSDA adapts to new dynamics via Fourier space adaptation.
problem Generalizing to unseen dynamical systems with limited data.
method Automatic partitioning of known environments in Fourier modes and adaptation of specific modes for new environments.
result FNSDA achieves superior or competitive generalization performance with reduced parameter cost.
Study on geometry and dynamics of transverse subgroups.
problem Understanding the geometry and dynamics of transverse subgroups.
method Survey of recent research on semi-simple Lie groups.
result Recent findings on transverse subgroups of semi-simple Lie groups.
Dynamic risk assessment method for WUI fires improves upon static frameworks.
problem Static risk assessment methods fail to capture dynamic changes in WUI fire risks.
method Dynamic evaluation matrix, grey incidence analysis, optimization model.
result The proposed method effectively captures dynamic risk evolution patterns.
Develops a method to model neural dynamics with flexible yet interpretable latent states.
problem Capturing complex nonlinear dynamics in neural time series while maintaining interpretability.
method Gaussian Process Switching Linear Dynamical System (gpSLDS) that balances expressiveness and interpretability.
result Favorable performance in comparison to rSLDS on synthetic and real neuroscience data.
SINDy-PI robustly identifies implicit dynamics from noisy data.
problem Accurately modeling nonlinear dynamics from noisy data.
method Parallel, implicit SINDy algorithm with multiple optimization algorithms and model selection.
result Significantly more noise robust than previous SINDy approaches.