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.
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.
Bayesian filtering approach identifies nonlinear restoring forces in dynamic systems.
problem Identification of nonlinear dynamic systems in engineering.
method Modeling the nonlinear restoring force as a Gaussian process, converting it to a state-space model, and inferring internal states and the nonlinear restoring force through filtering and smoothing.
result The approach effectively identifies nonlinear restoring forces in both simulated and experimental datasets.
PenduMAV is a 6-input omnidirectional MAV without internal forces.
problem Designing a MAV without internal forces and structural costs.
method Multibody dynamics derivation, SE(3) control, Lyapunov analysis, Gazebo simulations.
result Asymptotic stabilization of the closed-loop system under parametric uncertainty and actuator noise.
ITF improves DSR but inflates curvature, while marginal likelihood reduces it, affecting QoIs.
problem Curvature mismatch between teacher forcing and marginal likelihood in chaotic dynamical systems.
method Comparing objective-induced curvatures of ITF and marginal likelihood in a probabilistic switching augmentation of AL-RNNs.
result Curvature inflation by ITF and reduction by marginal likelihood affect dynamical quantities of interest.
Neural network models colloidal particle dynamics in non-equilibrium systems.
problem Analyzing non-equilibrium dynamics of many-body colloidal systems.
method Combining power functional theory and machine learning, training a neural network to predict internal force fields.
result The neural network accurately predicts dynamics in non-equilibrium systems, in good agreement with simulations.
Latent force models are systems whereby there is a mechanistic model describing the dynamics of the system state, with some unknown forcing term that is approximated with a Gaussian process. If such dynamics are non-linear, it can be difficult to estimate the posterior state and forcing term jointly, particularly when …
The paper integrates dissipative and curl forces using geometric methods.
problem Incorporating dissipative forces into curl forces for non-conservative systems.
method Geometric metriplectic approach, Herglotz principle, generalized Euler-Lagrange equation, Galley's method.
result Natural formulations for Lagrangian and Hamiltonian dynamics of non-conservative systems.
The Teacher Forcing algorithm trains recurrent networks by supplying observed sequence values as inputs during training and using the network's own one-step-ahead predictions to do multi-step sampling. We introduce the Professor Forcing algorithm, which uses adversarial domain adaptation to encourage the dynamics of th…
BoostMD accelerates molecular dynamics simulations by 8x with ML force fields.
problem Long inference times of ML force fields limit practical use in molecular dynamics.
method BoostMD uses previous time-step features to predict energies and forces, reducing complexity and computational cost.
result BoostMD achieves an 8-fold speedup and accurately samples the Boltzmann distribution.
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.
New insights into Hessian structure of neural networks reveal two forces.
problem Understanding the Hessian structure of neural networks.
method Analyzing the static and dynamic forces, comparing limit distributions using random matrix theory.
result The Hessian structure arises from a combination of static and dynamic forces, with C being a primary driver. We present a time-dependent Langevin description of dynamics of stock prices. Based on a simple sliding-window algorithm, the fluctuation of stock prices is discussed in the view of a time-dependent linear restoring force which is the linear approximation of the drift parameter in Langevin equation estimated from the f…
We apply the potential force estimation method to artificial time series of market price produced by a deterministic dealer model. We find that dealers' feedback of linear prediction of market price based on the latest mean price changes plays the central role in the market's potential force. When markets are dominated…
Neural networks' optimization dynamics are confined to a single basin despite connected basins in the loss landscape.
problem Neural networks' optimization dynamics are confined to a single basin despite connected basins in the loss landscape.
method Identifying entropic barriers arising from the interplay between curvature variations along low-loss paths and noise in optimization dynamics.
result Curvature-induced entropic forces bias noisy dynamics back toward the endpoints, explaining the confinement and connectivity of solutions.
Feature normalization prevents collapse in non-contrastive learning dynamics.
problem Non-contrastive learning can collapse into a single point due to lack of repulsive force.
method Extended previous theory based on L2 loss to cosine loss, considering feature normalization.
result Cosine loss induces stable equilibrium, preventing collapse even with insufficient repulsive force.
New algorithm efficiently trains machine learning models to atomic forces data.
problem Efficiently training machine learning models to large amounts of force data.
method Developed an efficient algorithm for training machine learning models to all available force data.
result Training to all available force data is only a few times more expensive than training to energies alone.
Given a real vector space V of finite dimension, together with a particular homogeneous field of bivectors that we call a "field of projective forces", we define a law of dynamics such that the position of the particle is a "ray" i.e. a half-line drawn from the origin of V. The impulsion is a bivector whose support is …
Study calculates curvature for fluid dynamics group, proving positivity.
problem Analyzing curvature in fluid dynamics groups with Coriolis force.
method Calculates Misiolek curvature of central extension group.
result Positivity of sectional curvature implies existence of conjugate points.
Study reveals hidden infections and infection dynamics from early data.
problem Understanding early infection dynamics and hidden infections in COVID-19.
method Data-driven machine learning analysis focusing on infection counts over time.
result Significant asymptomatic infections, 10-day lag, and strong infectious force.
Paper introduces a PDE-free method for decomposing forces in any dimension.
problem Analyzing non-conservative forces in arbitrary dimensions.
method Geometric decomposition using homotopy operator and Frobenius theorem.
result Decomposes forces into gradient and antiexact components, characterizing curl forces.
Latent force models (LFM) are principled approaches to incorporating solutions to differential equations within non-parametric inference methods. Unfortunately, the development and application of LFMs can be inhibited by their computational cost, especially when closed-form solutions for the LFM are unavailable, as is …
Framework predicts responses in misspecified systems using GPLFM and BNNs.
problem Predicting responses in dynamical systems with model misspecification.
method Integrates GPLFM and BNNs for uncertainty-aware inference and prediction.
result Systematic propagation of uncertainty from diagnosis to prediction.
Proposes a new model to price options considering market forces beyond Black-Scholes.
problem Tackles the limitations of the Black-Scholes model in capturing unexpected market behaviors.
method Uses the analogy between quantum harmonic oscillator and financial market dynamics to propose a new market force-driven model.
result Shows how various market forces can be incorporated to modify option pricing, providing practical applications.
RFC enhances humanoid control to imitate complex human motions.
problem Dynamics mismatch between humanoid models and real humans.
method Residual Force Control (RFC) augments control policies with external forces.
result RFC outperforms state-of-the-art methods in convergence speed and motion quality.
Smooth flows for physical systems with smooth energies and forces.
problem Smooth energies for physical simulations and force computation.
method Smooth mixture transformations on compact intervals and hypertori, using root-finding and the inverse function theorem.
result Smooth flows allow training by force matching and use as molecular dynamics potentials.
Weibull weight-scale parameter λ evolves during AdamW training, with alignment, injection, and decay forces driving its growth and relaxation.
problem Understanding the evolution of the Weibull weight-scale parameter λ during AdamW training. method Deriving a leading-order three-force decomposition of the squared weight norm from AdamW updates.
result The alignment force dominates the rise phase, contributing 88-94% of the absolute force budget across four random seeds.
Study active nematic forces on curved surfaces, revealing new coupling mechanisms.
problem Understanding active nematic forces on curved surfaces.
method Developed a thermodynamically consistent surface model with nematic activity, analyzed topological defects.
result Active defects contribute both tangential and normal forces on curved surfaces.
Paper models market dynamics using bull and bear forces.
problem Complex market dynamics influenced by biases and narratives.
method Bias to Behavior from Bull-Bear Dynamics (B4) model.
result Model predicts market trends with superior performance and interpretable insights.
New method improves sample diversity and efficiency from complex distributions.
problem Sampling from intractable un-normalized distributions with high auto-correlation.
method Stein self-repulsive dynamics using a repulsive force to push samples away from past trajectories.
result Significantly decreases auto-correlation and increases effective sample size.
The dynamics defined by a force field which is positively homogeneous of degree −3 can always be reduced, by simply constraining it. The dimension of the phase space is reduced by two dimensions, while it may only be reduced by one dimension if the degree of homogeneity is different from −3. This remark is an elega…
We develop an efficient sampling method by simulating Langevin dynamics with an artificial force rather than a natural force by using the gradient of the potential energy. The standard technique for sampling following the predetermined distribution such as the Gibbs-Boltzmann one is performed under the detailed balance…
We investigate the large-fluctuation dynamics in financial markets, based on the minute-to-minute and daily data of the Chinese Indices and German DAX. The dynamic relaxation both before and after the large fluctuations is characterized by a power law, and the exponents p± usually vary with the strength of the lar…
Bayesian modelling of dynamic systems must achieve a compromise between providing a complete mechanistic specification of the process while retaining the flexibility to handle those situations in which data is sparse relative to model complexity, or a full specification is hard to motivate. Latent force models achieve …
Unified framework connects two market-making models, revealing their underlying equivalence.
problem Independent calibration of two market-making frameworks (Avellaneda-Stoikov and Cartea-Jaimungal).
method Axiomatic approach to market preference functional, showing equivalence under specific conditions.
result Avellaneda-Stoikov and Cartea-Jaimungal frameworks are equivalent under certain conditions.
In this thesis, we consider the suitability of using the charged cold fluid model in the description of ultra-relativistic beams. The method that we have used is the following. Firstly, the necessary notions of kinetic theory and differential geometry of second order differential equations are explained. Then an averag…
AniDS improves molecular force field modeling by learning anisotropic noise.
problem Molecular force field modeling suffers from oversimplified assumptions about atomic motions.
method AniDS introduces anisotropic noise generation for better modeling of directional and structural variability.
result AniDS outperforms existing methods on benchmarks, achieving significant improvements in force prediction accuracy.
The paper explains emergent phenomena in deep learning using entropic forces.
problem Understanding the cause of emergent phenomena in deep learning and large language models.
method Proposes a rigorous entropic-force theory for neural networks trained with SGD and variants.
result Shows that representation learning is governed by emergent entropic forces that break continuous symmetries and preserve discrete ones.
For many externally driven complex systems neither the noisy driving force, nor the internal dynamics are a priori known. Here we focus on systems for which the time dependent activity of a large number of components can be monitored, allowing us to separate each signal into a component attributed to the external drivi…
Formula for the force field of Newtonian dynamical systems admitting the normal shift of hypersurfaces in Riemannian manifolds is considered. Problem of globalization for geometric structures associated with this formula is studied.
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.
HCLM framework uses entropy regularization for open learning systems.
problem Real-world AI challenges and limitations of deep learning.
method Dynamical and information-theoretic framework with entropy regularization.
result Geometric entropy surrogates, especially log-determinant covariance entropy, induce stronger and more stable information forces.
Trained recurrent networks are powerful tools for modeling dynamic neural computations. We present a target-based method for modifying the full connectivity matrix of a recurrent network to train it to perform tasks involving temporally complex input/output transformations. The method introduces a second network during…
Model reduction methods aim to describe complex dynamic phenomena using only relevant dynamical variables, decreasing computational cost, and potentially highlighting key dynamical mechanisms. In the absence of special dynamical features such as scale separation or symmetries, the time evolution of these variables typi…
Topological surgery occurs in natural phenomena where two points are selected and attracting or repelling forces are applied. The two points are connected via an invisible `thread'. In order to model topologically such phenomena we introduce dynamics in 1-, 2- and 3-dimensional topological surgery, by means of attracti…
In this paper we contribute a novel algorithm family, which generalizes many unsupervised techniques including unnormalized and energy models, and allows us to infer different statistical modalities (e.g. data likelihood and ratio between densities) from data samples. The proposed unsupervised technique, named Probabil…
Li-York theorem tells us that a period 3 orbit for a continuous map of the interval into itself implies the existence of a periodic orbit of every period. This paper concerns an analogue of the theorem for homeomorphisms of the 2-dimensional disk. In this case a periodic orbit is specified by a braid type and on the se…
New gauge fields modify Fokker-Planck dynamics without changing the stationary state.
problem Understanding and modifying nonreversible dynamics in Fokker-Planck models.
method Formulate nonreversible perturbations as gauge fields, mapping to supersymmetric Hamiltonians, and learning finite forces.
result Learned finite forces can recover the optimal Lyapunov-equation solution in nonconvex landscapes.