Hamiltonian Neural Networks

By Sam Greydanus, Misko Dzamba, Jason Yosinski. 2019

1,264 citations recorded by the source corpus.

Even though neural networks enjoy widespread use, they still struggle to learn the basic laws of physics. How might we endow them with better inductive biases? In this paper, we draw inspiration from Hamiltonian mechanics to train models that learn and respect exact conservation laws in an unsupervised manner. We evaluate our models on problems where conservation of energy is important, including the two-body problem and pixel observations of a pendulum. Our model trains faster and generalizes better than a regular neural network. An interesting side effect is that our model is perfectly reversible in time.

Subfields: Artificial Intelligence, Materials Chemistry, Statistical and Nonlinear Physics

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Materials Chemistry

In Statistical and Nonlinear Physics

Citations in the corpus

Hamiltonian Generative Networks (2019, methodology): “The ﬁrst question was recently addressed by the Hamiltonian Neural Network (HNN) (Greydanus et al., 2019) approach, which was able to learn the Hamiltonian of three simple physical systems from noisy phase space observations.”
Discovering Symbolic Models from Deep Learning with Inductive Biases (2020, methodology): “This model is a combination of a Hamiltonian Neural Network [45, 46] and GN.”
Lagrangian Neural Networks (2020, background): “2019), but with the objective of learning a Lagrangian rather than a Hamiltonian so not to restrict the learned kinetic energy.”
Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems (2020, background): “The Hamiltonian operator in physics is the primary tool for modeling the time evolution of systems with conserved quantities, but until recently the formalism had not been integrated with NNs. Greydanus et al. [112] design a NN architecture that naturally learns and respects energy conservation and ”
Integrating Physics-Based Modeling with Machine Learning: A Survey (2020, background): “…in Toth et al. [249], where they show that not only can NNs learn the Hamiltonian, but also the abstract phase space (assumed to be known in Greydanus et al. [98]) to more effectively model expressive densities in similar physical systems and also extend more generally to other problems in physics.”
Universal Differential Equations for Scientific Machine Learning (2020, methodology): “[14] Sam Greydanus, Misko Dzamba, and Jason Yosinski.”
Continuous-in-Depth Neural Networks (2020, background): “Due to their popularity, there is a rich body of work that aims to explain “why” shortcut connections between layers enables the training of very deep NNs [73, 4, 29, 48, 51, 44].”
Characterizing possible failure modes in physics-informed neural networks (2021, background): “Some approaches have focused on embedding specialized physical constraints into NNs, such as conservation of energy or momentum [4, 12] or multiscale features [34].”
Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control (2019, methodology): “A more recent (concurrent) work by Greydanus et al. (2019) uses Hamiltonian mechanics to learn the dynamics of autonomous, energy-conserved mechanical systems from time-series data of position, momentum, and their derivatives.”
Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers (2020, background): “Other studies have investigated the similarities of dynamical systems and deep learning methods [65] and employed conservation laws to learn systems described by Hamiltonian mechanics [18, 12].”