From 01fde188315dfc5726f7c0f3cc7393e31347c5de Mon Sep 17 00:00:00 2001 From: Aman Desai <98302868+amanmdesai@users.noreply.github.com> Date: Sun, 18 Sep 2022 15:24:44 +0530 Subject: [PATCH] minor typo fixes --- intro-teaser.ipynb | 12 ++++++------ overview.md | 2 +- 2 files changed, 7 insertions(+), 7 deletions(-) diff --git a/intro-teaser.ipynb b/intro-teaser.ipynb index b46786d..945a3f1 100644 --- a/intro-teaser.ipynb +++ b/intro-teaser.ipynb @@ -15,7 +15,7 @@ "source": [ "Let's start with a very reduced example that highlights some of the key capabilities of physics-based learning approaches. Let's assume our physical model is a very simple equation: a parabola along the positive x-axis.\n", "\n", - "Despite being very simple, there are two solutions for every point along x, i.e. we have two modes, one above the other one below the x-axis, as shown on the left below. If we don't take care a conventional learning approach will give us an approximation like the red one shown in the middle, which is completely off. With an improved learning setup, ideally, by using a discretized numerical solver, we can at least accurately represent one of the modes of the solution (shown in green on the right).\n", + "Despite being very simple, there are two solutions for every point along x, i.e. we have two modes, one above the other one below the x-axis, as shown on the left below. If we don't take care, a conventional learning approach will give us an approximation like the red one shown in the middle, which is completely off. With an improved learning setup, ideally, by using a discretized numerical solver, we can at least accurately represent one of the modes of the solution (shown in green on the right).\n", "\n", "```{figure} resources/intro-teaser-side-by-side.png\n", "---\n", @@ -198,7 +198,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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", 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" ] @@ -274,7 +274,7 @@ "id": "conscious-budapest", "metadata": {}, "source": [ - "The loss function is the crucial point for training: we directly incorporate the function f into the loss. In this simple case, the `loss_dp` function simply computes the square of the prediction `y_pred`. \n", + "The loss function is the crucial point for training: we directly incorporate the function $f$ into the loss. In this simple case, the `loss_dp` function simply computes the square of the prediction `y_pred`. \n", "\n", "Later on, a lot more could happen here: we could evaluate finite-difference stencils on the predicted solution, or compute a whole implicit time-integration step of a solver. Here we have a simple _mean-squared error_ term of the form $|y_{\\text{pred}}^2 - y_{\\text{true}}|^2$, which we are minimizing during training. It's not necessary to make it so simple: the more knowledge and numerical methods we can incorporate, the better we can guide the training process." ] @@ -339,7 +339,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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" ] @@ -375,7 +375,7 @@ "\n", "- We're still only getting one side of the curve! This is to be expected because we're representing the solutions with a deterministic function. Hence, we can only represent a single mode. Interestingly, whether it's the top or bottom mode is determined by the random initialization of the weights in $f$ - run the example a couple of times to see this effect in action. To capture multiple modes we'd need to extend the NN to capture the full distribution of the outputs and parametrize it with additional dimensions.\n", "\n", - "- The region with $x$ near zero is typically still off in this example. The network essentially learns a linear approximation of one half of the parabola here. This is partially caused by the weak neural network: it is very small and shallow. In addition, the evenly spread of sample points along the x-axis bias the NN towards the larger y values. These contribute more to the loss, and hence the network invests most of its resources to reduce the error in this region.\n" + "- The region with $x$ near zero is typically still off in this example. The network essentially learns a linear approximation of one half of the parabola here. This is partially caused by the weak neural network: it is very small and shallow. In addition, the evenly spread of sample points along the x-axis bias the NN towards the larger $y$ values. These contribute more to the loss, and hence the network invests most of its resources to reduce the error in this region.\n" ] }, { @@ -389,7 +389,7 @@ "\n", "Good and obvious examples are bifurcations in fluid flow. Smoke rising above a candle will start out straight, and then, due to tiny perturbations in its motion, start oscillating in a random direction. The images below illustrate this case via _numerical perturbations_: the perfectly symmetric setup will start turning left or right, depending on how the approximation errors build up. Averaging the two modes would give an unphysical, straight flow similar to the parabola example above.\n", "\n", - "Similarly, we have different modes in many numerical solutions, and typically it's important to recover them, rather than averaging them out. Hence, we'll show how to leverage training via _differentiable physics_ in the following chapters for more practical and complex cases.\n", + "Similarly, we have different modes in many numerical solutions, and typically it's important to recover them, rather than averaging them out. Hence, we'll show how to leverage training via _differentiable physics_ in the following chapters for more practical and complex cases.\n", "\n", "```{figure} resources/intro-fluid-bifurcation.jpg\n", "---\n", diff --git a/overview.md b/overview.md index 8b837de..6c33b63 100644 --- a/overview.md +++ b/overview.md @@ -119,7 +119,7 @@ where a solver targets cases from a certain well-defined problem domain repeatedly, it can for instance make a lot of sense to once invest significant resources to train a neural network that supports the repeated solves. Based on the -domain-specific specialization of this network, such a hybrid +domain-specific specialization of this network, such a hybrid solver could vastly outperform traditional, generic solvers. And despite the many open questions, first publications have demonstrated that this goal is not overly far away {cite}`um2020sol,kochkov2021`.