11 research outputs found
Constrained Deep Learning-based Model Predictive Control with Improved Constraint Satisfaction
Machine learning technique can help reduce computational cost of model
predictive control (MPC). In this paper, a constrained deep neural networks
design is proposed to learn and construct MPC policies for nonlinear input
affine dynamic systems. Using constrained training of neural networks helps
enforce MPC constraints effectively. We show the asymptotic stability of the
learned policies. Additionally, different data sampling strategies are compared
in terms of their generalization errors on the learned policy. Furthermore,
probabilistic feasibility and optimality guarantees are provided for the
learned control policy. The proposed algorithm is implemented on a rotary
inverted pendulum experimentally and control performance is demonstrated and
compared with the exact MPC and the normally trained learning MPC. The results
show that the proposed algorithm improves constraint satisfaction while
preserves computational efficiency of the learned policy
Physics-Informed Neural Networks for Minimising Worst-Case Violations in DC Optimal Power Flow
Physics-informed neural networks exploit the existing models of the
underlying physical systems to generate higher accuracy results with fewer
data. Such approaches can help drastically reduce the computation time and
generate a good estimate of computationally intensive processes in power
systems, such as dynamic security assessment or optimal power flow. Combined
with the extraction of worst-case guarantees for the neural network
performance, such neural networks can be applied in safety-critical
applications in power systems and build a high level of trust among power
system operators. This paper takes the first step and applies, for the first
time to our knowledge, Physics-Informed Neural Networks with Worst-Case
Guarantees for the DC Optimal Power Flow problem. We look for guarantees
related to (i) maximum constraint violations, (ii) maximum distance between
predicted and optimal decision variables, and (iii) maximum sub-optimality in
the entire input domain. In a range of PGLib-OPF networks, we demonstrate how
physics-informed neural networks can be supplied with worst-case guarantees and
how they can lead to reduced worst-case violations compared with conventional
neural networks.Comment: The code to reproduce all simulation results is available online in
https://github.com/RahulNellikkath/Physics-Informed-Neural-Network-for-DC-OP
On the Use of Neural Networks for Full Waveform Inversion
Neural networks have recently gained attention in solving inverse problems.
One prominent methodology are Physics-Informed Neural Networks (PINNs) which
can solve both forward and inverse problems. In the paper at hand, full
waveform inversion is the considered inverse problem. The performance of PINNs
is compared against classical adjoint optimization, focusing on three key
aspects: the forward-solver, the neural network Ansatz for the inverse field,
and the sensitivity computation for the gradient-based minimization. Starting
from PINNs, each of these key aspects is adapted individually until the
classical adjoint optimization emerges. It is shown that it is beneficial to
use the neural network only for the discretization of the unknown material
field, where the neural network produces reconstructions without oscillatory
artifacts as typically encountered in classical full waveform inversion
approaches. Due to this finding, a hybrid approach is proposed. It exploits
both the efficient gradient computation with the continuous adjoint method as
well as the neural network Ansatz for the unknown material field. This new
hybrid approach outperforms Physics-Informed Neural Networks and the classical
adjoint optimization in settings of two and three-dimensional examples
Physics-informed neural networks with hard constraints for inverse design
Inverse design arises in a variety of areas in engineering such as acoustic,
mechanics, thermal/electronic transport, electromagnetism, and optics. Topology
optimization is a major form of inverse design, where we optimize a designed
geometry to achieve targeted properties and the geometry is parameterized by a
density function. This optimization is challenging, because it has a very high
dimensionality and is usually constrained by partial differential equations
(PDEs) and additional inequalities. Here, we propose a new deep learning method
-- physics-informed neural networks with hard constraints (hPINNs) -- for
solving topology optimization. hPINN leverages the recent development of PINNs
for solving PDEs, and thus does not rely on any numerical PDE solver. However,
all the constraints in PINNs are soft constraints, and hence we impose hard
constraints by using the penalty method and the augmented Lagrangian method. We
demonstrate the effectiveness of hPINN for a holography problem in optics and a
fluid problem of Stokes flow. We achieve the same objective as conventional
PDE-constrained optimization methods based on adjoint methods and numerical PDE
solvers, but find that the design obtained from hPINN is often simpler and
smoother for problems whose solution is not unique. Moreover, the
implementation of inverse design with hPINN can be easier than that of
conventional methods
Structure-preserving neural networks
We develop a method to learn physical systems from data that employs feedforward neural networks and whose predictions comply with the first and second principles of thermodynamics. The method employs a minimum amount of data by enforcing the metriplectic structure of dissipative Hamiltonian systems in the form of the so-called General Equation for the Non-Equilibrium Reversible-Irreversible Coupling, GENERIC (Ăttinger and Grmela (1997) [36]). The method does not need to enforce any kind of balance equation, and thus no previous knowledge on the nature of the system is needed. Conservation of energy and dissipation of entropy in the prediction of previously unseen situations arise as a natural by-product of the structure of the method. Examples of the performance of the method are shown that comprise conservative as well as dissipative systems, discrete as well as continuous ones
A Stochastic Sequential Quadratic Optimization Algorithm for Nonlinear Equality Constrained Optimization with Rank-Deficient Jacobians
A sequential quadratic optimization algorithm is proposed for solving smooth
nonlinear equality constrained optimization problems in which the objective
function is defined by an expectation of a stochastic function. The algorithmic
structure of the proposed method is based on a step decomposition strategy that
is known in the literature to be widely effective in practice, wherein each
search direction is computed as the sum of a normal step (toward linearized
feasibility) and a tangential step (toward objective decrease in the null space
of the constraint Jacobian). However, the proposed method is unique from others
in the literature in that it both allows the use of stochastic objective
gradient estimates and possesses convergence guarantees even in the setting in
which the constraint Jacobians may be rank deficient. The results of numerical
experiments demonstrate that the algorithm offers superior performance when
compared to popular alternatives