PhysicsOptimizer

PhysicsOptimizer(parameters, objective, constraints) (pinneapple_core.optim, also pp.PhysicsOptimizer) states a constrained design or calibration problem once and solves it with any of six methods. Every method returns the same OptimizeResult (parameters, value, largest constraint violation, feasibility, evaluations, family, history, time).

from pinneapple_core.optim import PhysicsOptimizer, eq, ineq

opt = PhysicsOptimizer({"a": (0.5, 2.0, 1.6), "b": (0.5, 2.0, 0.8)},         # name: (lo, hi, start)
                       objective=lambda x: -rigidity(x),                     # torch function of the vector x
                       constraints=[eq(lambda x: x[0] * x[1] - 1.0)])        # a*b = 1
opt.minimize("slsqp")                     # or "adjoint", "penalty", "augmented_lagrangian", "differential_evolution", "bayesian"
opt.compare()                             # all of them on the same problem

Method	Family	Needs
slsqp	sequential quadratic programming with autograd gradients of objective and constraints	torch objective
adjoint	the same SQP with the objective gradient you supply (an adjoint solve, implicit_solve, torch.func.grad)	grad=
penalty	projected Adam on the objective plus a growing quadratic penalty	torch objective
augmented_lagrangian	projected Adam with multiplier updates, so constraints are met exactly	torch objective
differential_evolution	population search; equality constraints as a thin band of width tol/2	nothing
bayesian	Gaussian-process expected improvement times the probability of feasibility, one GP per constraint	nothing

Constraints are ineq(fn) for fn(x) <= 0 and eq(fn) for fn(x) == 0; a function may return a vector. With backend="numpy" the functions are plain numpy and gradient methods use finite differences; argument="dict" passes the parameters by name. A point is feasible when every violation is at most tol (default 1e-3); an impossible problem is reported as feasible=False, never hidden.

Reference problem

examples/physics_optimizer/01_constrained_shape_six_methods.py: the torsional rigidity (integral of u for -laplace(u) = 1, u = 0 on the boundary) of an a x b rectangle from the differentiable finite-element solver, maximised at fixed area. The square a = b = 1 is the known optimum. All six methods find it:

Method	a, b	value	violation	evaluations
slsqp	1, 1	-0.0340297	1e-14	17
adjoint	1, 1	-0.0340297	1e-14	17
penalty	1.001, 0.999	-0.0340298	3e-6	3001
augmented_lagrangian	1, 1	-0.0340297	2e-9	2001
differential_evolution	1, 1	-0.0340637	5e-4	605
bayesian	0.998, 1.003	-0.0340975	1e-3	61

The gradient methods are the cheapest in evaluations when gradients exist; Bayesian optimisation reaches the same answer in 61 evaluations without gradients, which is the one to use when each evaluation is an expensive simulation. Optimal control and MPC are not part of this interface (roadmap X32); the existing pinneapple_design.design_optimizer pipeline is unchanged.