New method combines neural networks with Monte Carlo for complex system reliability.
problem Estimating small failure probabilities in complex systems.
method Subset Simulation with Hamiltonian Neural Networks.
result High acceptance rates and computational efficiency in low-probability regions.
Proposes NSSNNs to predict nonseparable Hamiltonian systems.
problem Predicting nonseparable Hamiltonian systems with coupled dynamics.
method Augmented symplectic time integrator to decouple position and momentum.
result Long-term, accurate, and robust predictions for large-scale Hamiltonian systems.
Hamiltonian Monte Carlo on ReLU networks is inefficient due to large local error.
problem Inefficiency of Hamiltonian Monte Carlo on ReLU neural networks.
method Analysis of Hamiltonian Monte Carlo with leapfrog integrator for Bayesian neural network inference.
result Leapfrog HMC for ReLU networks has a large local error rate of Ω(ε), leading to inefficiency. We propose Symplectic Recurrent Neural Networks (SRNNs) as learning algorithms that capture the dynamics of physical systems from observed trajectories. An SRNN models the Hamiltonian function of the system by a neural network and furthermore leverages symplectic integration, multiple-step training and initial state op…
Physics-enhanced NNs improve predictive accuracy in small data scenarios.
problem Predicting physical systems dynamics with limited data.
method Integrating physical principles (Hamiltonian/Lagrangian) and regularization term based on energy level into neural networks.
result Significant gains in predictive accuracy for small data cases.
HDNNs can approximate any continuous function, proving their expressivity.
problem Lack of a comprehensive study on the expressivity of HDNNs.
method Discretization of Hamiltonian Neural Ordinary Differential Equations (HNN-ODEs).
result HDNNs can approximate any continuous function over a compact domain.
Enhances HNNs for conservative systems with noisy data.
problem Modeling conservative systems with neural networks.
method Proposes a deep hidden physics model for continuous-time trajectory estimation.
result Integration scheme works well for HNNs, especially with low sampling rates.
Deep learning enhances Hamiltonian Monte Carlo for sampling gauge field configurations.
problem Sampling from complex gauge field topologies efficiently.
method Stacked neural networks to generalize Hamiltonian Monte Carlo.
result Significantly reduces computational cost for generating gauge field configurations.
Recurrent neural networks (RNNs) have gained a great deal of attention in solving sequential learning problems. The learning of long-term dependencies, however, remains challenging due to the problem of a vanishing or exploding hidden states gradient. By exploring further the recently established connections between RN…
The Hamiltonian formalism plays a central role in classical and quantum physics. Hamiltonians are the main tool for modelling the continuous time evolution of systems with conserved quantities, and they come equipped with many useful properties, like time reversibility and smooth interpolation in time. These properties…
SSINNs learn Hamiltonian systems from data with interpretable, low-memory models.
problem Learning Hamiltonian dynamical systems from data efficiently and accurately.
method Combines fourth-order symplectic integration with sparse regression for a learned Hamiltonian.
result Outperforms state-of-the-art techniques in system prediction and energy conservation.
Meta learning enables cross-domain Hamiltonian dynamics.
problem Adapting to new physical systems with different laws.
method Graph Neural Network (GNN) with meta learning.
result Unified Hamiltonian representation across multiple system domains.
New method uses symmetric splitting for efficient HMC inference in large neural networks.
problem Efficient inference for Bayesian neural networks with large datasets.
method Introduces a symmetric integration scheme for Hamiltonian Monte Carlo (HMC) that does not rely on stochastic gradients.
result Symmetric splitting leads to more efficient HMC inference over large data sets.
Simplifies neural network models by explicitly enforcing constraints in Cartesian coordinates.
problem Learning dynamics of complex systems efficiently and accurately.
method Embedding systems into Cartesian coordinates and using Lagrange multipliers to enforce constraints.
result Explicitly enforcing constraints leads to a 100x improvement in accuracy and data efficiency.
Canonical transformation plays a fundamental role in simplifying and solving classical Hamiltonian systems. We construct flexible and powerful canonical transformations as generative models using symplectic neural networks. The model transforms physical variables towards a latent representation with an independent harm…
Hybrid approach combines VI and HMC for efficient Bayesian inference in neural networks.
problem Computational demands and inaccuracies in Bayesian inference for neural networks.
method Combines VI and HMC, reducing parameter space and accelerating inference.
result Significantly reduces inference time for large neural networks, improving uncertainty quantification.
This work explores using deep NNs to learn quantum systems from probability distributions.
problem Learning quantum systems from limited probability distribution data.
method Using deep neural networks to reconstruct quantum Hamiltonian from probability distributions.
result Deep neural networks can learn quantum Hamiltonians from probability distributions.
New methods solve min-max problems on manifolds using Riemannian Hamiltonians.
problem Min-max optimization on Riemannian manifolds.
method Riemannian Hamiltonian methods (RHM) to minimize the Hamiltonian function.
result RHM leads to correct search directions and global optimality in min-max problems.
Bayesian model averaging fails under covariate shift, affecting neural networks' performance.
problem Bayesian model averaging's failure in neural networks under covariate shift.
method Explained the issue and proposed novel priors to improve robustness.
result Bayesian model averaging is problematic under covariate shift, especially with linear feature dependencies.
Neural networks are discrete entities: subdivided into discrete layers and parametrized by weights which are iteratively optimized via difference equations. Recent work proposes networks with layer outputs which are no longer quantized but are solutions of an ordinary differential equation (ODE); however, these network…
Develops neural networks for learning physics of complex systems by enforcing thermodynamics principles.
problem Learning physics of complex systems from incomplete experimental data.
method Integrates port-metriplectic formalism with neural networks to enforce thermodynamics principles.
result Neural networks can learn physics of complex systems by parts, reducing learning burden.
LNNs learn Lagrangians without canonical coordinates, conserving energy and relativity.
problem Neural networks struggle to learn physical symmetries like conservation laws.
method Lagrangian Neural Networks (LNNs) parameterize arbitrary Lagrangians using neural networks.
result LNNs conserve energy and relativity in complex systems.
A new neural network improves the accuracy of predicting constants of motion.
problem Discovering constants of motion in dynamical systems.
method A novel neural network architecture using SVD and a two-phase training algorithm.
result The new approach retains advantages of COMET and improves performance.
GeoHNN models physics laws for stable, accurate predictions.
problem Violations of physical principles in machine learning models.
method Explicitly encodes geometric priors in inertia and phase space.
result Significantly outperforms existing models in long-term stability and accuracy.
We consider the problem of learning an interpretable potential energy function from a Hamiltonian system's trajectories. We address this problem for classical, separable Hamiltonian systems. Our approach first constructs a neural network model of the potential and then applies an equation discovery technique to extract…
Paper presents a method to summarize HMC samples for neural networks, providing meaningful uncertainty estimates.
problem Lack of interpretable summary statistics for HMC samples in neural networks due to permutation symmetry.
method Introducing a transpositions metric to quantify permutations and using rebasin method to summarize HMC samples.
result Compact representation of HMC samples provides meaningful uncertainty estimates for each weight in a neural network.
LDDNN learns physical dynamics from data without exact solutions.
problem Learning physical dynamics from data without exact solutions.
method LDDNN topology that learns Lagrangian density from data.
result LDDNN can learn physical dynamics from data.
Paper analyzes SGHMC for non-convex optimization with discontinuous gradients.
problem Training neural networks with ReLU activation.
method Non-asymptotic convergence analysis of SGHMC with discontinuous gradients.
result Explicit upper bounds for expected excess risk in non-convex optimization.
We present a general-purpose method to train Markov chain Monte Carlo kernels, parameterized by deep neural networks, that converge and mix quickly to their target distribution. Our method generalizes Hamiltonian Monte Carlo and is trained to maximize expected squared jumped distance, a proxy for mixing speed. We demon…
Neural networks solve high-dimensional HJB PDEs with asymptotic guarantees.
problem Solving high-dimensional Hamilton-Jacobi-Bellman PDEs in stochastic control theory.
method Actor-critic machine learning algorithm with a structured critic and biased gradient actor.
result The training dynamics converge to an ODE, ensuring solutions to the original problem.
Bayesian framework discovers interpretable Lagrangian from data.
problem Discovering physical laws from limited data.
method Sparse Bayesian approach for learning interpretable Lagrangian.
result Automates Hamiltonian discovery from Lagrangian and provides ODE/PDE descriptions.
L-HNNs improve Bayesian inference by reducing gradient requirements and improving ESS.
problem Efficient Bayesian inference with complex target densities.
method Latent Hamiltonian Neural Networks (L-HNNs) with NUTS, incorporating online error monitoring.
result L-HNNs in NUTS with online error monitoring required 1--2 orders of magnitude fewer numerical gradients and improved ESS by an order of magnitude.
Bayesian deep learning tackles uncertainty in high-dimensional systems.
problem Uncertainty quantification in high-dimensional stochastic partial differential equations.
method Bayesian neural network (BNN) and Hamiltonian Monte Carlo (HMC) for efficient sampling of posterior distributions.
result The method efficiently handles high-dimensional problems with almost independent computational cost.
L-HNNs improve Bayesian inference efficiency by reducing gradient computation.
problem Efficient Bayesian inference with minimal gradient computation.
method Integrating L-HNNs into NUTS with online error monitoring.
result L-HNNs in NUTS outperform NUTS in complex posterior densities.
Physics-informed learning framework for pH systems and EB-PBC control.
problem Control of port-Hamiltonian systems from trajectory data.
method Co-learning of pH system model and EB-PBC through alternating optimization.
result Proven stability and robustness of the learned controller.
The translation equivariance of convolutional layers enables convolutional neural networks to generalize well on image problems. While translation equivariance provides a powerful inductive bias for images, we often additionally desire equivariance to other transformations, such as rotations, especially for non-image d…
New method uses kernel methods to approximate ground states of quantum Hamiltonians efficiently.
problem Approximating ground states of quantum Hamiltonians using neural networks is computationally expensive.
method Introduces a statistical learning approach using kernel methods to make optimization trivial.
result Ground state properties of arbitrary gapped quantum Hamiltonians can be reached with polynomial resources.
Study improves neural network calibration for drug discovery.
problem Improper calibration of neural network predictions in drug discovery.
method Compared different metrics for model hyperparameter tuning and proposed Bayesian Linear Probing (BLP) method.
result Bayesian Linear Probing (BLP) improves model calibration and accuracy.
A new decentralized Bayesian learning method using Metropolis-adjusted Hamiltonian Monte Carlo.
problem Decentralized Bayesian learning with uncertainty quantification.
method Metropolis-adjusted Hamiltonian Monte Carlo in a decentralized federated learning setting.
result Theoretical guarantees and numerical effectiveness of the method on non-convex problems.
Bayesian neural networks show complex posterior distributions that HMC can capture effectively.
problem Understanding and approximating the high-dimensional, non-convex posterior of Bayesian neural networks.
method Full-batch Hamiltonian Monte Carlo (HMC) on modern architectures.
result HMC provides a robust and comparable representation of the BNN posterior, with significant performance gains over standard training and deep ensembles.
New approach relaxes inductive biases of physics-inspired NNs for better performance.
problem Challenges in applying physics-inspired NNs to real-world systems.
method Examined and relaxed inductive biases of Hamiltonian NNs, improving performance on non-conservative systems.
result Improved performance on practical, non-conservative systems by relaxing inductive biases.
Estimating predictive uncertainty is crucial for many computer vision tasks, from image classification to autonomous driving systems. Hamiltonian Monte Carlo (HMC) is an sampling method for performing Bayesian inference. On the other hand, Dropout regularization has been proposed as an approximate model averaging techn…
We propose a new sampling method, the thermostat-assisted continuously-tempered Hamiltonian Monte Carlo, for Bayesian learning on large datasets and multimodal distributions. It simulates the Nosé-Hoover dynamics of a continuously-tempered Hamiltonian system built on the distribution of interest. A significant advantag…
New dataset abla2DFT for drug-like molecules benchmarks neural network potentials.
problem Lack of large, diverse datasets for training neural network potentials in quantum chemistry.
method Developed a new dataset abla2DFT containing energies, forces, and molecular properties for drug-like molecules. result First dataset with relaxation trajectories for drug-like molecules.
SON learns SPDE solutions and uncertainty from noisy data.
problem Uncertainty quantification in SPDEs with unknown model uncertainties.
method Combining DeepONet and SNNs, SON models stochasticity and predicts uncertainty.
result SON accurately captures solution structure and quantifies predictive uncertainty.
New algorithm optimizes MCMC sampling for structural dynamic models.
problem Time-consuming retraining of neural networks in MCMC methods.
method Adaptive meta-learning SGHMC algorithm that optimizes sampling strategy.
result Trained sampler can be applied to various problems without retraining.
Direct neural ratio estimator for likelihood-free inference.
problem Efficient likelihood estimation for complex models.
method Amortized likelihood ratio estimation using neural networks.
result DNRE often outperforms previous ratio estimators.
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.