D2PCCA integrates deep learning and probabilistic modeling for nonlinear dynamical systems.
problem Analyzing nonlinear dynamical systems with probabilistic understanding.
method Combines deep learning and probabilistic modeling, using KL annealing and normalizing flows.
result Captures latent dynamics in sequential datasets with improved convergence and flexibility.
Stable deep models learn dynamical systems with formal stability guarantees.
problem Difficulties in making formal claims about stability of deep network dynamics models.
method Jointly learning a dynamics model and Lyapunov function to ensure non-expansiveness.
result Proposes an approach for stable deep learning of dynamical systems.
This work studies learning dynamics in SSMs, linking them to deep linear networks.
problem Lack of theoretical understanding of SSMs, especially in deep state spaces.
method Analyzes learning dynamics of linear SSMs, focusing on frequency domain, and establishes links to deep linear networks.
result Analytical solutions for SSM learning dynamics under mild assumptions, linking to deep linear networks.
dynoGP uses deep Gaussian processes for dynamic system identification.
problem System identification for complex dynamical systems.
method Interconnecting linear dynamic GPs and static GPs to model dynamic and static nonlinearities.
result Demonstrates effectiveness of the approach using both simulated and real-world data.
Deep learning predicts contagion dynamics on complex networks.
problem Forecasting contagion dynamics on complex networks is challenging.
method Graph neural network learns local mechanisms from time series data.
result Deep learning offers new and accurate models of contagion dynamics.
Deep learning predicts dynamics from sparse data.
problem Predicting spatiotemporal dynamics from sparse data.
method Spatially dimension-independent deep learning framework.
result Predicts dynamics from sparse data sites.
DeepEDM forecasts time series by learning dynamics from embeddings.
problem Precise future prediction of complex nonlinear time series.
method Integrates nonlinear dynamical systems modeling with deep neural networks.
result DeepEDM outperforms state-of-the-art methods in forecasting accuracy.
Study models forest transitions with deep learning for parameter estimation.
problem Complex dynamics of forest, agricultural, and abandoned lands.
method Developed a stochastic differential equation model and used deep learning for parameter estimation.
result Deep learning approach estimates model parameters from time-series data.
Proposes DLGPD model to learn dynamics from images for planning.
problem Planning in unknown, indirectly observable environments.
method Deep latent Gaussian process dynamics model trained jointly with neural networks.
result Demonstrates improved data efficiency and transfer learning.
Deep RL solves complex macroeconomic models.
problem Solving dynamic stochastic general equilibrium models with bounded rationality.
method Using deep reinforcement learning to model agents as neural networks.
result Artificially intelligent agents can solve models in all policy regimes.
Use simplified layerwise linear models to understand neural dynamics.
problem Complex neural network dynamics are hard to grasp.
method Apply simplified layerwise linear models to explain neural phenomena.
result Simplified models explain neural collapse, emergence, etc.
Deep learning models learn chaotic system dynamics from real and simulated data.
problem Training deep learning models for chaotic systems requires big data.
method Jointly train deep neural networks on real and simulated data, enforcing physical laws.
result Proposes knowledge-based deep learning (KDL) for accurate forecasting of chaotic systems.
Deep RL optimizes dynamic portfolio weights in China's stock market.
problem Traditional portfolio optimization methods struggle with dynamic asset weight adjustments.
method Developed a deep reinforcement learning framework with novel reward functions and random sampling.
result Model outperforms traditional methods in portfolio optimization and risk mitigation.
New approach uses compressible dynamics to train deep models efficiently.
problem Efficient training of deep overparameterized models with low-rank structures.
method Leveraging low-dimensional structures and compressible dynamics within model parameters.
result Improved training efficiency and reduced overfitting in language models.
Deep learning models converge to Gaussian dynamics with mixed structured inputs.
problem Understanding neural network dynamics with complex input distributions.
method Extended hidden manifold model to Gaussian mixtures, analyzed via SGD.
result Learning dynamics with mixed inputs converge to Gaussian behavior.
Deep learning predicts NFT prices with high accuracy.
problem Dynamic valuation of non-fungible tokens (NFTs).
method Trained deep learning model on Ethereum blockchain data.
result Highly accurate price predictions of NFTs.
Physics-guided model improves deep learning for nonlinear systems.
problem Intractable inference of nonlinear dynamical systems from data.
method Physics-guided Deep Markov Model (PgDMM) using neural networks.
result Improved performance on nonlinear systems with structured latent space.
Complex high dimensional stochastic dynamic systems arise in many applications in the natural sciences and especially biology. However, while these systems are difficult to describe analytically, "snapshot" measurements that sample the output of the system are often available. In order to model the dynamics of such sys…
PhICNet combines physics and deep learning for forecasting and source identification in dynamical systems.
problem Forecasting and identifying unobservable external sources in spatio-temporal dynamical systems.
method Physics-Incorporated Convolutional Recurrent Neural Network (PhICNet).
result PhICNet can forecast dynamics and identify sources for relatively long periods.
Improves adversarial robustness of DEQ models by regulating neural dynamics.
problem Limited adversarial robustness of DEQ models.
method Interprets DEQs as neural dynamics, uses entropy reduction and random intermediate states.
result Significantly increases adversarial robustness of DEQ models.
A novel deep probabilistic model for dynamic systems forecasting.
problem Probabilistic forecasting in dynamic systems.
method Combining deep generative models and state space models with recurrent neural networks and variational sequence models.
result Outperforms existing models in system identification benchmarks and real-world centrifugal compressor forecasting.
New model explains deep learning performance at large learning rates.
problem Understanding deep learning performance at different learning rates.
method Developed neural networks with solvable training dynamics.
result Large learning rates lead to convergence to flatter minima.
Efficiently compress overparameterized deep models by focusing on low-dimensional learning dynamics.
problem Overparameterized models increase computational and memory costs.
method Study of learning dynamics reveals updates occur within a low-dimensional subspace, leading to a compression algorithm.
result Compressed deep linear networks converge faster and yield smaller recovery errors.
Researchers dissect Neural ODEs to understand their dynamics.
problem Understanding the inner workings of Neural ODEs.
method Developing continuous-depth formulation to clarify design choices.
result Clarified the influence of design choices on Neural ODE dynamics.
Paper proposes deep learning model for dynamic stock repurchase forecasting.
problem Complex temporal dependencies in corporate financial conditions.
method Hybrid Temporal Convolutional Network (TCN) and Attention-based LSTM.
result Model significantly outperforms static baselines in stock repurchase forecasting.
Dissipative SymODEN learns dynamics with dissipation and control from data.
problem Learning dynamics with dissipation and control from observed data.
method Dissipative SymODEN encodes port-Hamiltonian dynamics into a deep learning architecture.
result The learned model reveals key aspects of the system, such as inertia, dissipation, and potential energy.
Improved deep dynamics models with symmetries for better accuracy and generalization.
problem Limited physical accuracy and inability to generalize under distributional shift in deep learning dynamics models.
method Incorporating symmetries into convolutional neural networks using various methods tailored to enforce different symmetries.
result Models robust to distributional shift by symmetry group transformations and favorable sample complexity.
Deep learning adapts HVAC models to new buildings.
problem Adapting thermal dynamics models to new buildings with limited data.
method Deep supervised domain adaptation (DSDA) using LSTM-based Sequence to Sequence model.
result Deep supervised domain adaptation improves predictive performance over learning from scratch.
Proposes a method to forecast non-stationary time series.
problem Challenges of non-stationary conditional distributions in deep learning.
method Bayesian dynamic model + deep conditional distribution model.
result Adapts to non-stationary time series better than state-of-the-art solutions.
Proposes a deep learning method for modeling dynamic individual-level latent trajectories with changing parameters.
problem Modeling longitudinal data with changing individual-level dynamics parameters.
method Combines deep learning for dimensionality reduction and differential equations for dynamic modeling, allowing different parameters for sub-periods.
result Successfully identifies dynamic parameters and predictors of resilience.
This paper compares model-based and model-free control methods using neural networks.
problem Comparing model-based and model-free control methods for unknown nonlinear systems.
method Utilizes Deep Koopman Representation (DKRC) and Deep Deterministic Policy Gradient (DDPG) for control.
result DKRC outperforms DDPG in terms of control strategies and accuracy for unknown dynamics.
Deep learning improves low-fidelity dynamical models with scarce high-fidelity data.
problem Improving low-fidelity models with limited high-fidelity data.
method Transfer learning using a deep neural network to correct a low-fidelity model.
result An improved DNN model with high accuracy to underlying dynamics.
New model combines physics and machine learning for ocean dynamics.
problem Discovering hidden laws governing ocean dynamics.
method Develops Deep Neural Numerical Models (DNNMs) to learn hidden variables of physical laws.
result Illustrates DNNMs applied to Sea Surface Height dynamics, connecting to QG model.
Paper introduces a new volatility model for natural gas markets and discusses swing option pricing.
problem Modeling price and storage dynamics in natural gas markets with path-dependent volatility.
method Developed a novel stochastic path-dependent volatility model and used deep learning for swing option pricing.
result Proposed a deep learning method for numerical approximations of swing option pricing.
Deep learning networks are approximated using dynamical systems theory.
problem Understanding the approximation capabilities of deep learning networks.
method Modeling deep residual networks as continuous-time dynamical systems and using approximation theories in Lp. result Established general sufficient conditions for universal approximation of deep residual networks.
Method learns latent dynamics of complex systems from noisy data.
problem Challenging to construct ROMs from noisy high-dimensional data.
method Recurrent stochastic variational deep kernel learning (SVDKL).
result Framework accurately predicts system evolution in low-dimensional latent spaces.
Deep model integrates MRI and DTI for autism severity prediction.
problem Predicting spectrum-level deficits in autism using multimodal brain imaging.
method Generative deep-learning framework combining rs-fMRI and DTI data.
result Hybrid model outperforms existing methods in predicting autism severity.
New method for efficient probabilistic deep state-space models.
problem Efficient inference for probabilistic deep state-space models.
method Deterministic inference algorithm for ProDSSM with neural network weights.
result Superior balance between predictive performance and computational budget.
Framework augments physical models with deep learning for complex dynamics forecasting.
problem Forecasting complex dynamical phenomena with partial knowledge.
method APHYNITY framework: decomposes dynamics into physical and data-driven components.
result Framework accurately forecasts system evolution and identifies relevant parameters.
The paper analyzes the training dynamics of neural networks using kernel methods.
problem Understanding the training dynamics of neural networks in high-dimensional settings.
method High-dimensional asymptotics and gradient flow on kernel least-squares objectives.
result The training dynamics of neural networks undergo three stages, characterized by behaviors in the Oracle and Empirical worlds.
Deep learning models can infer individual trajectories from sparse data.
problem Learning individual dynamics from limited data points.
method Combining variational autoencoders (VAEs) with ordinary differential equations (ODEs) for dynamic modeling.
result Deep learning can recover individual trajectories from sparse data, but requires careful adaptation.
DAMNETS generates complex network dynamics models.
problem Generating flexible and scalable models for network time series is challenging.
method Deep autoregressive model for Markovian network time series.
result DAMNETS outperforms other methods in sample quality.
DBGDGM models dynamic brain graphs for better understanding brain function.
problem Previous brain graph models ignore temporal dynamics, limiting their usefulness.
method DBGDGM clusters brain regions into evolving communities and learns dynamic node embeddings.
result DBGDGM outperforms baselines in graph generation, dynamic link prediction, and graph classification.
Method learns low-dim. state vars from noisy high-dim. data.
problem Discovering dynamical models from noisy high-dimensional data.
method Stochastic Variational Deep Kernel Learning with encoder and latent model.
result Effective denoising, compact state representation, and uncertainty quantification.
Model-based reinforcement learning (RL) algorithms can attain excellent sample efficiency, but often lag behind the best model-free algorithms in terms of asymptotic performance. This is especially true with high-capacity parametric function approximators, such as deep networks. In this paper, we study how to bridge th…
Deep Bayesian models estimate causal effects for dynamic treatment regimes over long follow-up times.
problem Challenges in causal effect estimation for dynamic treatment regimes with long follow-up times.
method Combining outcome regression models with deep Bayesian models for high-dimensional features.
result Stable and accurate dynamic causal effect estimation from observational data, especially with long-term follow-up.
Two new Koopman models improve nonlinear system prediction.
problem Predicting nonlinear, nonconvex dynamic systems.
method Convex and Extended Koopman Models using deep learning.
result Significantly improved predictive performance.
SGD in DLNs reveals feature learning dynamics.
problem Understanding SGD dynamics in DLNs during saddle-to-saddle training.
method Stochastic Langevin dynamics with anisotropic, state-dependent noise; one-dimensional per-mode SDEs; Boltzmann distribution approximation.
result SGD noise encodes feature learning progression but does not alter saddle-to-saddle dynamics.